Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A locally simply connected space and fundamental groups of one point unions of cones
HTML articles powered by AMS MathViewer

by Katsuya Eda PDF
Proc. Amer. Math. Soc. 116 (1992), 239-249 Request permission

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) ${\pi _1}\left ( {\left ( {X,x} \right ) \vee \left ( {X,x} \right ),x} \right )$ is naturally isomorphic to the free product ${\pi _1}\left ( {X,x} \right ) * {\pi _1}\left ( {X,x} \right )$; (3) ${\pi _1}\left ( {\left ( {CX,x} \right ) \vee \left ( {CX,x} \right ),x} \right )$ is trivial. There exists a simply connected, locally simply connected Tychonoff space $X$ with $x \in X$, such that $\left ( {X,x} \right ) \vee \left ( {X,x} \right )$ is not simply connected.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55Q20, 57M05
  • Retrieve articles in all journals with MSC: 55Q20, 57M05
Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 116 (1992), 239-249
  • MSC: Primary 55Q20; Secondary 57M05
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1132409-0
  • MathSciNet review: 1132409