Paper Citation Record · LEDGER

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces

As of 21 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2412.11011.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2412.11011 v2

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T15:30:15.989730Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

36 of 36 outbound references displayed

verified exact4
verified fuzzy20
unresolved12
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9c216b43-eddb-45bf-b592-c17aa4597e4c · outbound

This paper cites Beattie and H.P.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Beattie and H.P

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:30:16.479030Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7fc8919a-00b6-4866-9325-56efa00ae173 · outbound

This paper cites Continuous Convergence on C(X).

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Continuous Convergence on C(X)

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:30:16.465173Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 18d85c21-54ed-4b88-9275-c05cadc06f90 · outbound

This paper cites Topology and Geometry.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Topology and Geometry

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:30:16.453114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b00b6ed3-6cfe-4d36-86ef-3c445bd273b2 · outbound

This paper cites an unresolved cited work.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-11T15:30:16.441254Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4967d4c4-554c-4a2e-8141-b455ff7ab567 · outbound

This paper cites Topology and groupoids.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Topology and groupoids

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:30:16.427522Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 56b73bdb-93e1-4bac-ad05-f1da411fec97 · outbound

This paper cites an unresolved cited work.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-11T15:30:16.414934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation c263713e-1512-4d56-b17d-e4a69e31f33b · outbound

This paper cites an unresolved cited work.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-11T15:30:16.402510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 35729df9-9664-4ae4-9044-12e2b3034b61 · outbound

This paper cites Dolecki and F.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Dolecki and F

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:30:16.390710Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 6ffa582a-5d57-410d-ac82-8c7cc28accf6 · outbound

This paper cites Epitopological and pseudotopological fundamental group functors.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Epitopological and pseudotopological fundamental group functors

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-11T15:30:16.099072Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7425926a-e00e-4829-b7de-364e40bcd79d · outbound

This paper cites General Topology.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces General Topology

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:30:16.378868Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 03fde1f2-4a51-43d7-93df-35bd1821be4a · outbound

This paper cites Grundstrukturen der Analysis I.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Grundstrukturen der Analysis I

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:30:16.368277Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 17263fb8-e90b-4dbb-bfde-01251d84a8a7 · outbound

This paper cites Algebraic Topology.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Algebraic Topology

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-11T15:30:15.895934Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d6e8c5be-b631-4b34-b223-f0832b741bbd · outbound

This paper cites Set Theory: The Third Millennium Edition, revised and expanded.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Set Theory: The Third Millennium Edition, revised and expanded

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:30:16.351130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 1dd93b06-317d-4cb3-b9b6-6a7e93612380 · outbound

This paper cites Introduction to Algebraic Topology.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Introduction to Algebraic Topology

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:30:16.340514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 08d867c1-4ed1-4c88-a8be-6dfd6d071f5b · outbound

This paper cites Kat ˇetov.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Kat ˇetov

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:30:16.328849Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d0685465-1c70-4a43-9126-d38207e6d97c · outbound

This paper cites an unresolved cited work.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-11T15:30:16.316076Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 01c02f77-38b2-4731-aa64-418a0bb40b93 · outbound

This paper cites Kennison.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Kennison

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:30:16.303024Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 414eaa55-00f3-4b96-852e-81d8940228c8 · outbound

This paper cites Basic Category Theory.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Basic Category Theory

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:30:16.289821Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0914e489-48dd-44bb-a975-f7611932d28b · outbound

This paper cites an unresolved cited work.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-11T15:30:16.275537Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0e28fb76-5e8e-4c45-9d82-f35055ff9457 · outbound

This paper cites The directed Vietoris-Rips complex and homotopy and singular homology groups of finite digraphs.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces The directed Vietoris-Rips complex and homotopy and singular homology groups of finite digraphs

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-11T15:30:15.927897Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ea66e8e7-34d3-4497-90b9-19987516ad26 · outbound

This paper cites A net theoretic approach to homotopy theory.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces A net theoretic approach to homotopy theory

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-08-11T15:30:16.067033Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 56e9ca8b-38f5-4489-99ea-7801eaa1dd31 · outbound

This paper cites an unresolved cited work.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-11T15:30:16.264722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 1600e7b7-a9ef-425f-8f25-4cc5149d3ded · outbound

This paper cites Continuity Theory.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Continuity Theory

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:30:16.253926Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 944653ca-6762-4209-8ac5-badcaef4446f · outbound

This paper cites O’Brien, M.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces O’Brien, M

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:30:16.241719Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2f196d70-b4d8-4924-be10-dced98bc8169 · outbound

This paper cites an unresolved cited work.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-11T15:30:16.230125Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ba1cb727-f365-45be-83c1-b9ccf39cde38 · outbound

This paper cites Convergence of evenly continuous nets in general function spaces.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Convergence of evenly continuous nets in general function spaces

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:30:16.217070Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 024aa4fe-f516-4d59-8a74-679d055d9324 · outbound

This paper cites an unresolved cited work.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-11T15:30:16.204927Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation abb62139-5086-4975-a113-0007c83e0593 · outbound

This paper cites Some algebraically topological aspects in the realm of convenient topology.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Some algebraically topological aspects in the realm of convenient topology

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:30:16.193386Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 490e3a28-6cb3-4e1b-ba4c-b1dbc16ddfd8 · outbound

This paper cites ˇCech closure spaces: A unified framework for discrete and continuous homotopy.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces ˇCech closure spaces: A unified framework for discrete and continuous homotopy

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:30:16.181032Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 92d370c3-ca04-4180-8484-96a4a03b44a1 · outbound

This paper cites Cofibration and Model Category Structures for Discrete and Continuous Homotopy.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Cofibration and Model Category Structures for Discrete and Continuous Homotopy

Reference 30

Resolution: verified exact; local_arxiv, observed 2026-08-11T15:30:16.049278Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4dc1136d-6aea-40c8-b211-a38315fb57ed · outbound

This paper cites An Introduction to the Language of Category Theory.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces An Introduction to the Language of Category Theory

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:30:16.166265Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7c4242aa-d4a0-449f-989f-24bd58d644bf · outbound

This paper cites Handbook of Analysis and Its Foundations.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Handbook of Analysis and Its Foundations

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:30:16.152701Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation aaa66698-96f7-4db7-9eb5-6efdf261911b · outbound

This paper cites an unresolved cited work.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-11T15:30:16.139268Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4195c090-a480-4ef2-86b2-574cc0315f59 · outbound

This paper cites Universal Coverings for Limit and Pseudotopological Spaces.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Universal Coverings for Limit and Pseudotopological Spaces

Reference 34

Resolution: verified exact; local_arxiv, observed 2026-08-11T15:30:16.029718Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 1150864b-3109-4f63-b2e6-352b6932eb92 · outbound

This paper cites an unresolved cited work.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-11T15:30:16.126814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 04d73e65-963d-4328-bc83-b472ceef751f · outbound

This paper cites Topological spaces.

Algebraic Topology Without Open Sets: A Net Approach to Homotopy Theory in Limit Spaces Topological spaces

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:30:16.112173Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

No inbound Pith citation observations are available.