Displaying similar documents to “On weakly monotonically monolithic spaces”

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....

Mapping theorems on ℵ -spaces

Masami Sakai (2008)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we improve some mapping theorems on ℵ -spaces. For instance we show that an ℵ -space is preserved by a closed and countably bi-quotient map. This is an improvement of Yun Ziqiu’s theorem: an ℵ -space is preserved by a closed and open map.

Short proofs of two theorems in topology

Mohammad Ismail, Andrzej Szymański (1993)

Commentationes Mathematicae Universitatis Carolinae

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We present short and elementary proofs of the following two known theorems in General Topology: (i) [H. Wicke and J. Worrell] A T 1 weakly δ θ -refinable countably compact space is compact. (ii) [A. Ostaszewski] A compact Hausdorff space which is a countable union of metrizable spaces is sequential.

Paratopological (topological) groups with certain networks

Chuan Liu (2014)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we discuss certain networks on paratopological (or topological) groups and give positive or negative answers to the questions in [Lin2013]. We also prove that a non-locally compact, k -gentle paratopological group is metrizable if its remainder (in the Hausdorff compactification) is a Fréchet-Urysohn space with a point-countable cs*-network, which improves some theorems in [Liu C., Metrizability of paratopological ( semitopological ) groups, Topology Appl. 159 (2012), 1415–1420], [Liu...