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A nice class extracted from C p -theory

Vladimir Vladimirovich Tkachuk (2005)

Commentationes Mathematicae Universitatis Carolinae

We study systematically a class of spaces introduced by Sokolov and call them Sokolov spaces. Their importance can be seen from the fact that every Corson compact space is a Sokolov space. We show that every Sokolov space is collectionwise normal, ω -stable and ω -monolithic. It is also established that any Sokolov compact space X is Fréchet-Urysohn and the space C p ( X ) is Lindelöf. We prove that any Sokolov space with a G δ -diagonal has a countable network and obtain some cardinality restrictions on subsets...

A remark on the tightness of products

Oleg Okunev (1996)

Commentationes Mathematicae Universitatis Carolinae

We observe the existence of a σ -compact, separable topological group G and a countable topological group H such that the tightness of G is countable, but the tightness of G × H is equal to 𝔠 .

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