Two properties of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> weaker than the Fréchet Urysohn property

We prove that if an ultrafilter L is not coherent to a Q-point, then each analytic non-sigma-bounded topological group G admits an increasing chain of its proper subgroups such that: (i) U_{a in b(L)} G_a=G; and $(ii)$ For every sigma-bounded subgroup H of G there exists a such that H is a subset of G_a. In case of the group Sym(w) of all permutations of w with the topology inherited from w^w this improves upon earlier results of S. Thomas

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Variations on a theorem of Arhangel’skii and Pytkeev

Pavlović

2010

Acta Math Hung

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We identify continuous real-valued functions on a Tychonoff space X with their (closed) graphs thus allowing for C(X) to naturally inherit the lower Vietoris topology from the ambient hyperspace. We then calculate a bitopological version of tightness using the weak Lindelöf numbers of finite powers of X. We also characterize bitopological versions of countable fan and strong fan tightness of the point-open topology with respect to the lower Vietoris topology on C(X) in terms of suitable covering properties of the powers X n formulated using the language of S1 and S fin selection principles.

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Two properties of Cp(X) weaker than the Fréchet Urysohn property

Cited by 16 publications

References 13 publications

Topological Properties of the Weak and Weak$$^*$$ Topologies of Function Spaces

Topological Properties of the Weak and Weak$$^*$$ Topologies of Function Spaces

On the length of chains of proper subgroups covering a topological group

Variations on a theorem of Arhangel’skii and Pytkeev

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