Sequential conditions and free topological groups
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- by Edward T. Ordman and Barbara V. Smith-Thomas PDF
- Proc. Amer. Math. Soc. 79 (1980), 319-326 Request permission
Abstract:
Most of the results in this paper concern relationships between sequential properties of a pointed topological space (X, p) and sequential properties of the Graev free topological group on X. In particular, it is shown that the free group over a sequential ${k_\omega }$-space is sequential, and that a nondiscrete sequential free group has sequential order equal to ${\omega _1}$ (the first uncountable ordinal). The free topological group on a space X which includes a convergent sequence contains a closed subspace homeomorphic to ${S_\omega }$, a previously studied homogeneous, zero-dimensional sequential space. Finally, it is shown that there is no topological group homeomorphic to ${S_\omega }$.References
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Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 79 (1980), 319-326
- MSC: Primary 54D55; Secondary 22A99, 54G20
- DOI: https://doi.org/10.1090/S0002-9939-1980-0565363-2
- MathSciNet review: 565363