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A continuous map f : X → Y induces a map of sets π0(f) : π0(X) → π0(Y), satisfying conditions on composite maps and identity maps.
“sense that a continuous map f : X → Y induces a map of sets π 0 (f ) : π 0 (X) → π 0 (Y ), satisfying certain obvious conditions on composite maps and identity maps.”
From Topology and data (2009) · cites this paper as [19]
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- Authors
- Curtis, E. B.
- Affiliations
- Aarhus University (DK)
- Corresponding author
- Curtis, Edward B
- ORCID
- Curtis, Edward B
- Venue
- Advances in Mathematics
- Publisher
- Elsevier BV
- Published
- 1971-04
- Volume
- 6
- Issue
- 2
- Pages
- 107-209
- ISSN
- 0001-8708 (ISSN-L)
- OpenAlex
- W1971238472
- Cited by
- 304
- References
- 29
- Citations by year
- 2026: 6 · 2025: 3 · 2024: 7 · 2023: 8 · 2022: 7 · 2021: 9 · 2020: 3 · 2019: 6 · 2018: 15 · 2017: 4 · 2016: 7 · 2015: 5 · 2014: 9 · 2013: 10 · 2012: 19
- FWCI
- 2.34
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Advances in Mathematics (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Homotopy and Cohomology in Algebraic Topology
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Advanced Combinatorial Mathematics
- Keywords
- simplicial sets, simplicial homotopy theory, homotopy theory
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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