A topological vector space is Fréchet-Urysohn if and only if it has bounded tightness
Kąkol, J. ; López Pellicer, L. ; Todd, A. R.
Bull. Belg. Math. Soc. Simon Stevin, Tome 16 (2009) no. 1, p. 313-317 / Harvested from Project Euclid
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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.
Publié le : 2009-05-15
Classification:  Fréchet-Urysohn space,  bounded tightness,  countable tightness,  $C_p(X)$ spaces,  46A30,  54C35 
@article{1244038142,
     author = {K\k akol, J. and L\'opez Pellicer, L. and Todd, A. R.},
     title = {A topological vector space is Fr\'echet-Urysohn if and only if it has
bounded tightness},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {16},
     number = {1},
     year = {2009},
     pages = { 313-317},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1244038142}
}

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, Tome 16 (2009) no. 1, pp.  313-317. http://gdmltest.u-ga.fr/item/1244038142/