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Displaying 61 – 71 of 71

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 $f (Ū) \subseteq \bar{f (U)}$ 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 $θ$ -continuous functions

F. Commaroto, T. Noiri (1986)

Matematički Vesnik

On $α$ -continuous functions

Dragan S. Janković, Ch. Konstadilaki-Savvopoulou (1992)

Mathematica Bohemica

Classes of functions continuous in various senses, in particular $θ$ -continuous, $α$ -continuous, feeblz continuous a.o., and relations between the classes, are studied.

On $α$ -continuous functions

Takashi Noiri (1984)

Časopis pro pěstování matematiky

On $β$ - $I$ -open sets and a decomposition of almost- $I$ -continuity.

Hatir, E., Noiri, T. (2006)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

On $θ$ -closed sets and some forms of continuity

Mohammad Saleh (2004)

Archivum Mathematicum

In this paper, we further the study of $θ$ -compactness a generalization of quasi-H-closed sets and its applications to some forms of continuity using $θ$ -open and $δ$ -open sets. Among other results, it is shown a weakly $θ$ -retract of a Hausdorff space $X$ is a $δ$ -closed subset of $X$ .

On $θ$ -continuity and strong $θ$ -continuity.

Saleh, Mohammed (2003)

Applied Mathematics E-Notes [electronic only]

On $θ$ -generalized closed sets.

Dontchev, Julian, Maki, Haruo (1999)

International Journal of Mathematics and Mathematical Sciences

On $θ$ -precontinuous functions.

Noiri, Takashi (2001)

International Journal of Mathematics and Mathematical Sciences

Openly factorizable spaces and compact extensions of topological semigroups

Taras O. Banakh, Svetlana Dimitrova (2010)

Commentationes Mathematicae Universitatis Carolinae

We prove that the semigroup operation of a topological semigroup $S$ extends to a continuous semigroup operation on its Stone-Čech compactification $β S$ provided $S$ is a pseudocompact openly factorizable space, which means that each map $f : S \to Y$ to a second countable space $Y$ can be written as the composition $f = g \circ p$ of an open map $p : X \to Z$ onto a second countable space $Z$ and a map $g : Z \to Y$ . We present a spectral characterization of openly factorizable spaces and establish some properties of such spaces.

Oscillations, quasi-oscillations and joint continuity.

Mirmostafaee, A.K. (2010)

Annals of Functional Analysis (AFA) [electronic only]

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