Covering maps for locally path-connected spaces

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dc.creatorBrodskiy, N.
dc.creatorDydak, J.
dc.creatorLabuz, B.
dc.creatorMitra, A.
dc.date2008-01-31
dc.date2008-02-14
dc.date.accessioned2026-07-07T09:20:25Z
dc.date.available2026-07-07T09:20:25Z
dc.descriptionWe define Peano covering maps and prove basic properties analogous to classical covers. Their domain is always locally path-connected but the range may be an arbitrary topological space. One of characterizations of Peano covering maps is via the uniqueness of homotopy lifting property for all locally path-connected spaces. Regular Peano covering maps over path-connected spaces are shown to be identical with generalized regular covering maps introduced by Fischer and Zastrow. If $X$ is path-connected, then every Peano covering map is equivalent to the projection $\widetilde X/H\to X$, where $H$ is a subgroup of the fundamental group of $X$ and $\widetilde X$ equipped with the basic topology. The projection $\widetilde X/H\to X$ is a Peano covering map if and only if it has the unique path lifting property. We define a new topology on $\widetilde X$ for which one has a characterization of $\widetilde X/H\to X$ having the unique path lifting property if $H$ is a normal subgroup of $π_1(X)$. Namely, $H$ must be closed in $π_1(X)$. Such groups include $π(\mathcal{U},x_0)$ ($\mathcal{U}$ being an open cover of $X$) and the kernel of the natural homomorphism from the fundamental group to the Cech fundamental group.
dc.description25 pages, several references added plus Proposition 4.12 and Example 4.13
dc.identifierhttps://arxiv.org/abs/0801.4967
dc.identifierhttp://arxiv.org/abs/0801.4967
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154714
dc.subjectGeometric Topology
dc.subjectAlgebraic Topology
dc.subjectGeneral Topology
dc.subject55Q52 (Primary); 55M10, 54E15 (Secondary)
dc.titleCovering maps for locally path-connected spaces
dc.typetext

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