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

Katsuya Eda

Research output: Contribution to journalArticle

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

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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