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On similarity between topologies

Artur Bartoszewicz, Małgorzata Filipczak, Andrzej Kowalski, Małgorzata Terepeta (2014)

Open Mathematics

Let T 1 and T 2 be topologies defined on the same set X and let us say that (X, T 1) and (X, T 2) are similar if the families of sets which have nonempty interior with respect to T 1 and T 2 coincide. The aim of the paper is to study how similar topologies are related with each other.

On some classes of spaces with the D -property

Juan Carlos Martínez (2014)

Commentationes Mathematicae Universitatis Carolinae

We shall prove that under CH every regular meta-Lindelöf P -space which is locally D has the D -property. In addition, we shall prove that a regular submeta-Lindelöf P -space is D if it is locally D and has locally extent at most ω 1 . Moreover, these results can be extended from the class of locally D -spaces to the wider class of 𝔻 -scattered spaces. Also, we shall give a direct proof (without using topological games) of the result shown by Peng [On spaces which are D, linearly D and transitively D, Topology...

On some fan-tightness type properties

J. Valuyeva (1998)

Commentationes Mathematicae Universitatis Carolinae

Properties similar to countable fan-tightness are introduced and compared to countable tightness and countable fan-tightness. These properties are also investigated with respect to function spaces and certain classes of continuous mappings.

On some kinds of fuzzy connected spaces

Qutaiba Ead Hassan (2007)

Applications of Mathematics

In this paper we introduce new results in fuzzy connected spaces. Among the results obtained we can mention the good extension of local connectedness. Also we prove that in a T 1 -fuzzy compact space the notions c-zero dimensional, strong c-zero dimensional and totally c i -disconnected are equivalent.

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