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.
@article{230dc1038a4743808aa15e52c8c603e4,
title = "A locally simply connected space and fundamental groups of one point unions of cones",
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.",
keywords = "Cone, First countable, Fundamental group, Locally simple, One point union",
author = "Katsuya Eda",
year = "1992",
doi = "10.1090/S0002-9939-1992-1132409-0",
language = "English",
volume = "116",
pages = "239--249",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "1",

}

TY - JOUR

T1 - A locally simply connected space and fundamental groups of one point unions of cones

AU - Eda, Katsuya

PY - 1992

Y1 - 1992

N2 - 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.

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.

KW - Cone

KW - First countable

KW - Fundamental group

KW - Locally simple

KW - One point union

UR - http://www.scopus.com/inward/record.url?scp=84966211913&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966211913&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1992-1132409-0

DO - 10.1090/S0002-9939-1992-1132409-0

M3 - Article

VL - 116

SP - 239

EP - 249

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -

Access to Document