A new version of homotopical Hausdorff

LaBuz, Brendon

doi:10.48550/arxiv.1104.0855

Cited by 2 publications

(1 citation statement)

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“…Therefore by Corollary 5.2 we have the following theorem that gives a family of Spanier spaces. follows from Proposition 2.4 of [8] which states that shape injectivity and small loop homotopically Hausdorffness are equivalent. Corollary 5.9.…”

Section: The Topology Of Spanier Subgroupsmentioning

confidence: 96%

Spanier spaces and covering theory of non-homotopically path Hausdorff spaces

Pakdaman,

Torabi,

Mashayekhy

2011

Preprint

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H. Fischer et al. (Topology and its Application, 158 (2011) 397-408.) introduced the Spanier group of a based space (X, x) which is denoted by π sp 1 (X, x). By a Spanier space we mean a space X such that π sp 1 (X, x) = π 1 (X, x), for every x ∈ X. In this paper, first we give an example of Spanier spaces. Then we study the influence of the Spanier group on covering theory and introduce Spanier coverings which are universal coverings in the categorical sense. Second, we give a necessary and sufficient condition for the existence of Spanier coverings for non-homotopically path Hausdorff spaces. Finally, we study the topological properties of Spanier groups and find out a criteria for the Hausdorffness of topological fundamental groups.

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Section: The Topology Of Spanier Subgroupsmentioning

confidence: 96%