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On natural metrics.

Claudi Alsina, Enric Trillas (1977)

Stochastica

In the present note we study the effective construction of a natural generalized metric structure (on a set), obtaining as particular case the result of Menger. In the case of groups, we analyze its topology and its structure of natural proximity space (in the sense of Efremovic).

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.

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