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On non-normality points, Tychonoff products and Suslin number

Sergei Logunov (2022)

Commentationes Mathematicae Universitatis Carolinae

Let a space X be Tychonoff product α < τ X α of τ -many Tychonoff nonsingle point spaces X α . Let Suslin number of X be strictly less than the cofinality of τ . Then we show that every point of remainder is a non-normality point of its Čech–Stone compactification β X . In particular, this is true if X is either R τ or ω τ and a cardinal τ is infinite and not countably cofinal.

On nonregular ideals and z -ideals in C ( X )

F. Azarpanah, M. Karavan (2005)

Czechoslovak Mathematical Journal

The spaces X in which every prime z -ideal of C ( X ) is either minimal or maximal are characterized. By this characterization, it turns out that for a large class of topological spaces X , such as metric spaces, basically disconnected spaces and one-point compactifications of discrete spaces, every prime z -ideal in C ( X ) is either minimal or maximal. We will also answer the following questions: When is every nonregular prime ideal in C ( X ) a z -ideal? When is every nonregular (prime) z -ideal in C ( X ) a z -ideal? For...

On nowhere first-countable compact spaces with countable π -weight

Jan van Mill (2015)

Commentationes Mathematicae Universitatis Carolinae

The minimum weight of a nowhere first-countable compact space of countable π -weight is shown to be κ B , the least cardinal κ for which the real line can be covered by κ many nowhere dense sets.

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