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On weak forms of preopen and preclosed functions

Miguel Caldas, Govindappa Navalagi (2004)

Archivum Mathematicum

In this paper we introduce two classes of functions called weakly preopen and weakly preclosed functions as generalization of weak openness and weak closedness due to [26] and [27] respectively. We obtain their characterizations, their basic properties and their relationshisps with other types of functions between topological spaces.

On weak κ -metric

Bandlow, Ingo (1984)

Proceedings of the 12th Winter School on Abstract Analysis

On weaker forms of the chain (F) condition and metacompactness-like covering properties in the product spaces

Süleyman Önal, Çetin Vural (2013)

Open Mathematics

We introduce the concept of a family of sets generating another family. Then we prove that if X is a topological space and X has W = {W(x): x ∈ X} which is finitely generated by a countable family satisfying (F) which consists of families each Noetherian of ω-rank, then X is metaLindelöf as well as a countable product of them. We also prove that if W satisfies ω-rank (F) and, for every x ∈ X, W(x) is of the form W 0(x) ∪ W 1(x), where W 0(x) is Noetherian and W 1(x) consists of neighbourhoods of...

On weakly bisequential spaces

Chuan Liu (2000)

Commentationes Mathematicae Universitatis Carolinae

Weakly bisequential spaces were introduced by A.V. Arhangel'skii [1], in this paper. We discuss the relations between weakly bisequential spaces and metric spaces, countably bisequential spaces, Fréchet-Urysohn spaces.

On weakly Gibson F σ -measurable mappings

Olena Karlova, Volodymyr Mykhaylyuk (2013)

Colloquium Mathematicae

A function f: X → Y between topological spaces is said to be a weakly Gibson function if f ( Ū ) f ( U ) ¯ for any open connected set U ⊆ X. We prove that if X is a locally connected hereditarily Baire space and Y is a T₁-space then an F σ -measurable mapping f: X → Y is weakly Gibson if and only if for any connected set C ⊆ X with dense connected interior the image f(C) is connected. Moreover, we show that each weakly Gibson F σ -measurable mapping f: ℝⁿ → Y, where Y is a T₁-space, has a connected graph.

On weakly infinite-dimensional subspuees

P. Borst (1992)

Fundamenta Mathematicae

We will construct weakly infinite-dimensional (in the sense of Y. Smirnov) spaces X and Y such that Y contains X topologically and d i m Y = ω 0 and d i m X = ω 0 + 1 . Consequently, the subspace theorem does not hold for the transfinite dimension dim for weakly infinite-dimensional spaces.

On Weakly Measurable Functions

Szymon Żeberski (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

We show that if T is an uncountable Polish space, 𝓧 is a metrizable space and f:T→ 𝓧 is a weakly Baire measurable function, then we can find a meagre set M ⊆ T such that f[T∖M] is a separable space. We also give an example showing that "metrizable" cannot be replaced by "normal".

On weakly monotonically monolithic spaces

Liang-Xue Peng (2010)

Commentationes Mathematicae Universitatis Carolinae

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.

On weak-open π -images of metric spaces

Zhaowen Li (2006)

Czechoslovak Mathematical Journal

In this paper, we give some characterizations of metric spaces under weak-open π -mappings, which prove that a space is g -developable (or Cauchy) if and only if it is a weak-open π -image of a metric space.

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