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

Katsuya Eda

Research output: Contribution to journal › Article

3 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 languageEnglish
Pages (from-to)239-249
Number of pages11
JournalProceedings of the American Mathematical Society
Volume116
Issue number1
DOIs
Publication statusPublished - 1992
Externally publishedYes

Fingerprint

Locally Connected
Fundamental Group
Cones
Union
Cone
First Countable
Free Product
Trivial
Isomorphic

Keywords

  • Cone
  • First countable
  • Fundamental group
  • Locally simple
  • One point union

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

A locally simply connected space and fundamental groups of one point unions of cones. / Eda, Katsuya.

In: Proceedings of the American Mathematical Society, Vol. 116, No. 1, 1992, p. 239-249.

Research output: Contribution to journal › Article

Eda, K 1992, 'A locally simply connected space and fundamental groups of one point unions of cones', Proceedings of the American Mathematical Society, vol. 116, no. 1, pp. 239-249. https://doi.org/10.1090/S0002-9939-1992-1132409-0
Eda K. A locally simply connected space and fundamental groups of one point unions of cones. Proceedings of the American Mathematical Society. 1992;116(1):239-249. https://doi.org/10.1090/S0002-9939-1992-1132409-0
Eda, Katsuya. / A locally simply connected space and fundamental groups of one point unions of cones. In: Proceedings of the American Mathematical Society. 1992 ; Vol. 116, No. 1. pp. 239-249.
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