Displaying similar documents to “New viewpoints, results and problems in the theory of Phragmén-Lindelöf”

Remainders of metrizable and close to metrizable spaces

A. V. Arhangel'skii (2013)

Fundamenta Mathematicae

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We continue the study of remainders of metrizable spaces, expanding and applying results obtained in [Fund. Math. 215 (2011)]. Some new facts are established. In particular, the closure of any countable subset in the remainder of a metrizable space is a Lindelöf p-space. Hence, if a remainder of a metrizable space is separable, then this remainder is a Lindelöf p-space. If the density of a remainder Y of a metrizable space does not exceed 2 ω , then Y is a Lindelöf Σ-space. We also show...

Uniformization and anti-uniformization properties of ladder systems

Todd Eisworth, Gary Gruenhage, Oleg Pavlov, Paul Szeptycki (2004)

Fundamenta Mathematicae

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Natural weakenings of uniformizability of a ladder system on ω₁ are considered. It is shown that even assuming CH all the properties may be distinct in a strong sense. In addition, these properties are studied in conjunction with other properties inconsistent with full uniformizability, which we call anti-uniformization properties. The most important conjunction considered is the uniformization property we call countable metacompactness and the anti-uniformization property we call thinness....

The union of two D-spaces need not be D

Dániel T. Soukup, Paul J. Szeptycki (2013)

Fundamenta Mathematicae

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We construct from ⋄ a T₂ example of a hereditarily Lindelöf space X that is not a D-space but is the union of two subspaces both of which are D-spaces. This answers a question of Arhangel'skii.