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A note on monotone countable paracompactness

Ge Ying, Chris Good (2001)

Commentationes Mathematicae Universitatis Carolinae

We show that a space is MCP (monotone countable paracompact) if and only if it has property ( * ) , introduced by Teng, Xia and Lin. The relationship between MCP and stratifiability is highlighted by a similar characterization of stratifiability. Using this result, we prove that MCP is preserved by both countably biquotient closed and peripherally countably compact closed mappings, from which it follows that both strongly Fréchet spaces and q-space closed images of MCP spaces are MCP. Some results on...

A note on operators extending partial ultrametrics

Edward D. Tymchatyn, Michael M. Zarichnyi (2005)

Commentationes Mathematicae Universitatis Carolinae

We consider the question of simultaneous extension of partial ultrametrics, i.e. continuous ultrametrics defined on nonempty closed subsets of a compact zero-dimensional metrizable space. The main result states that there exists a continuous extension operator that preserves the maximum operation. This extension can also be chosen so that it preserves the Assouad dimension.

A note on pseudobounded paratopological groups

Fucai Lin, Shou Lin, Iván Sánchez (2014)

Topological Algebra and its Applications

Let G be a paratopological group. Then G is said to be pseudobounded (resp. ω-pseudobounded) if for every neighbourhood V of the identity e in G, there exists a natural number n such that G = Vn (resp.we have G = ∪ n∈N Vn). We show that every feebly compact (2-pseudocompact) pseudobounded (ω-pseudobounded) premeager paratopological group is a topological group. Also,we prove that if G is a totally ω-pseudobounded paratopological group such that G is a Lusin space, then is G a topological group....

A Note on Regular-closed Functions

Takashi Noiri (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Se X ed Y sono spazi topologici, una funzione f : X → Y è detta regolarmente chiusa [5] se essa trasforma ogni insieme regolarmente chiuso di X in un insieme chiuso di Y . Si dimostra che una funzione regolarmente chiusa f : X → Y risulta chiusa se X è normale.

A note on ℵ -spaces and g -metrizable spaces

Zhaowen Li (2005)

Czechoslovak Mathematical Journal

In this paper, we give the mapping theorems on ℵ -spaces and g -metrizable spaces by means of some sequence-covering mappings, mssc-mappings and π -mappings.

A note on spaces with countable extent

Yan-Kui Song (2017)

Commentationes Mathematicae Universitatis Carolinae

Let P be a topological property. A space X is said to be star P if whenever 𝒰 is an open cover of X , there exists a subspace A ⊆ X with property P such that X = S t ( A , 𝒰 ) . In this note, we construct a Tychonoff pseudocompact SCE-space which is not star Lindelöf, which gives a negative answer to a question of Rojas-Sánchez and Tamariz-Mascarúa.

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