Variations on a theorem of Arhangel’skii and Pytkeev
Tóm tắt
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 S
1 and S
fin selection principles.
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