Bulletin of the Belgian Mathematical Society - Simon Stevin

A topological vector space is Fréchet-Urysohn if and only if it has bounded tightness

J. Kąkol, L. López Pellicer, and A. R. Todd

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Abstract

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

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 16, Number 2 (2009), 313-317.

Dates
First available in Project Euclid: 3 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1244038142

Digital Object Identifier
doi:10.36045/bbms/1244038142

Mathematical Reviews number (MathSciNet)
MR2541044

Zentralblatt MATH identifier
1180.46005

Subjects
Primary: 46A30: Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness) 54C35: Function spaces [See also 46Exx, 58D15]

Keywords
Fréchet-Urysohn space bounded tightness countable tightness $C_p(X)$ spaces

Citation

Kąkol, J.; López Pellicer, L.; Todd, A. R. A topological vector space is Fréchet-Urysohn if and only if it has bounded tightness. Bull. Belg. Math. Soc. Simon Stevin 16 (2009), no. 2, 313--317. doi:10.36045/bbms/1244038142. https://projecteuclid.org/euclid.bbms/1244038142


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