A locally simply connected space and fundamental groups of one point unions of cones

Katsuya Eda

doi:10.1090/S0002-9939-1992-1132409-0

A locally simply connected space and fundamental groups of one point unions of cones

Katsuya Eda

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

Let CX be the cone over a space X. Let a space X be first countable at x, then the following are equivalent: (1) X is locally simply connected at x; (2) Π₁((X, x) ⩗ (X, x), x) is naturally isomorphic to the free product Π₁(X, x)*Π₁ (X, x); (3) Π₁((CX, x)V(CX, x), x) is trivial. There exists a simply connected, locally simply connected Tychonoff space X with x ∈ X, such that (X, x) ⩗ (X, x) is not simply connected.

Original language	English
Pages (from-to)	239-249
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	116
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1992-1132409-0
Publication status	Published - 1992
Externally published	Yes

Keywords

Cone
First countable
Fundamental group
Locally simple
One point union

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-1992-1132409-0

Cite this

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AB - Let CX be the cone over a space X. Let a space X be first countable at x, then the following are equivalent: (1) X is locally simply connected at x; (2) Π1((X, x) ⩗ (X, x), x) is naturally isomorphic to the free product Π1(X, x)*Π1 (X, x); (3) Π1((CX, x)V(CX, x), x) is trivial. There exists a simply connected, locally simply connected Tychonoff space X with x ∈ X, such that (X, x) ⩗ (X, x) is not simply connected.

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KW - Fundamental group

KW - Locally simple

KW - One point union

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A locally simply connected space and fundamental groups of one point unions of cones

Abstract

Keywords

ASJC Scopus subject areas

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