Displaying similar documents to “On supertightness and function spaces”

On Manes' countably compact, countably tight, non-compact spaces

James Dabbs (2011)

Commentationes Mathematicae Universitatis Carolinae

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We give a straightforward topological description of a class of spaces that are separable, countably compact, countably tight and Urysohn, but not compact or sequential. We then show that this is the same class of spaces constructed by Manes [Monads in topology, Topology Appl. 157 (2010), 961--989] using a category-theoretical framework.

On weakly monotonically monolithic spaces

Liang-Xue Peng (2010)

Commentationes Mathematicae Universitatis Carolinae

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In this note, we introduce the concept of weakly monotonically monolithic spaces, and show that every weakly monotonically monolithic space is a D -space. Thus most known conclusions on D -spaces can be obtained by this conclusion. As a corollary, we have that if a regular space X is sequential and has a point-countable w c s * -network then X is a D -space.

A note on paratopological groups

Chuan Liu (2006)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, it is proved that a first-countable paratopological group has a regular G δ -diagonal, which gives an affirmative answer to Arhangel’skii and Burke’s question [, Topology Appl. (2006), 1917–1929]. If G is a symmetrizable paratopological group, then G is a developable space. We also discuss copies of S ω and of S 2 in paratopological groups and generalize some Nyikos [, Proc. Amer. Math. Soc. (1981), no. 4, 793–801] and Svetlichnyi [, Vestnik Moskov. Univ. Ser. I Mat. Mekh....