PreprintCC BY 4.0arXiv
Countable models of one-dimensional Peano continua
Abstract
In this paper, we prove that a one-dimensional Peano continuum X admits a weak homotopy equivalence X→ C to a countable space C if and only if the wild set w(X) is countable.
Related
- Plane separating continua inscribe rectangles
- Geometrically distinct unbounded continua of solutions for Yamabe-type equations
- Proper classes of non-embeddable continua
- Data-driven material data identification in micromorphic continua
- A posteriori controllability of non-linear remodelling in linear elastic continua
BibTeX
@misc{brazas2026countable,
title = {{Countable models of one-dimensional Peano continua}},
author = {Jeremy Brazas and Petar Pavesic},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35875},
eprint = {2610.35875},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35875},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Countable models of one-dimensional Peano continua
AU - Jeremy Brazas
AU - Petar Pavesic
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.35875
UR - https://arxiv.org/abs/2610.35875
AB - In this paper, we prove that a one-dimensional Peano continuum X admits a weak homotopy equivalence X→ C to a countable space C if and only if the wild set w(X) is countable.
ER -