Proceedings of the American Mathematical Society

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

 

 

Embedding the free group $ F(X)$ into $ F(\beta X)$


Authors: Temple H. Fay, M. Rajagopolan and Barbara V. Smith-Thomas
Journal: Proc. Amer. Math. Soc. 84 (1982), 297-302
MSC: Primary 22A05; Secondary 54D35
MathSciNet review: 637187
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Abstract: We show that for a Tychonoff space, $ X$ and the canonical embedding $ {\beta _X}:X \to \beta X$, the induced homomorphism $ F{\beta _X}:F(X) \to F(\beta X)$ is an embedding between the free topological groups when $ X$ has the property that $ {X^n}$ is pseudo-compact for all $ n \geqslant 1$. An application of this result is if $ X$ is such a space and $ \beta X$ is 0-dimensional, then $ F(X)$ is 0-dimensional.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0637187-0
Keywords: Free topological group, pseudocompact, Stone-Čech compactification, Tychonoff space
Article copyright: © Copyright 1982 American Mathematical Society