A note on mappings of Baire spaces
A note on monotone countable paracompactness
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 multivalued Baire category theorem
A note on nearly-paracompact spaces
A note on nonfragmentability of Banach spaces.
A note on open mappings of irreducible continua
A note on operators extending partial ultrametrics
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
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 realcompact unions
A Note on Regular-closed Functions
Se ed sono spazi topologici, una funzione è detta regolarmente chiusa [5] se essa trasforma ogni insieme regolarmente chiuso di in un insieme chiuso di . Si dimostra che una funzione regolarmente chiusa risulta chiusa se è normale.
A note on rings of continuous functions.
A note on semihomeomorphism between semi spaces
A note on separate continuity and connectivity properties
Separately continuous functions are shown to have certain properties related to connectedness.
A note on singularities in ANR's
A note on some applications of -open sets.
A note on “Some results on multi-valued weakly Jungck mappings in b-metric space”
The proofs of Theorems 2.1, 2.2 and 2.3 from [Olatinwo M.O., Some results on multi-valued weakly jungck mappings in b-metric space, Cent. Eur. J. Math., 2008, 6(4), 610–621] base on faulty evaluations. We give here correct but weaker versions of these theorems.
A note on -spaces and -metrizable spaces
In this paper, we give the mapping theorems on -spaces and -metrizable spaces by means of some sequence-covering mappings, mssc-mappings and -mappings.
A note on spaces with countable extent
Let be a topological property. A space is said to be star P if whenever is an open cover of , there exists a subspace with property such that . 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.
A note on spaces with locally countable weak-bases.
A note on the algebraic de Morgan's law