Embedding the free group $F(X)$ into $F(\beta X)$
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- by Temple H. Fay, M. Rajagopolan and Barbara V. Smith-Thomas
- Proc. Amer. Math. Soc. 84 (1982), 297-302
- DOI: https://doi.org/10.1090/S0002-9939-1982-0637187-0
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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.References
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Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 297-302
- MSC: Primary 22A05; Secondary 54D35
- DOI: https://doi.org/10.1090/S0002-9939-1982-0637187-0
- MathSciNet review: 637187