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May 2009 A topological vector space is Fréchet-Urysohn if and only if it hasbounded tightness
J. Kąkol, L. López Pellicer, A. R. Todd
Bull. Belg. Math. Soc. Simon Stevin 16(2): 313-317 (May 2009). DOI: 10.36045/bbms/1244038142

Abstract

We prove that a topological vector space $E$ is Fréchet-Urysohn if andonly if it has a bounded tightness, i.e. for any subset $A$ of $E$ and eachpoint $x$ in the closure of $A$ there exists a bounded subset of $A$ whoseclosure contains $x$. This answers a question of Nyikos on $C_p(X)$(personal communication). We also raise two related questions fortopological groups.

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J. Kąkol. L. López Pellicer. A. R. Todd. "A topological vector space is Fréchet-Urysohn if and only if it hasbounded tightness." Bull. Belg. Math. Soc. Simon Stevin 16 (2) 313 - 317, May 2009. https://doi.org/10.36045/bbms/1244038142

Information

Published: May 2009
First available in Project Euclid: 3 June 2009

zbMATH: 1180.46005
MathSciNet: MR2541044
Digital Object Identifier: 10.36045/bbms/1244038142

Subjects:
Primary: 46A30, 54C35‎

Rights: Copyright © 2009 The Belgian Mathematical Society

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Vol.16 • No. 2 • May 2009
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