<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Using ideals, we introduce a new class of topological spaces that are more general concept than <italic>R</italic>0 spaces [Cs´asz´ar, ´ A.: <italic>General Topology</italic>. Akad- ´emiai Kiad´o, Budapest, 1978]. Different properties will be studied for that class of topological spaces. We also define a new kind of convergence for sequences of functions and formulate more general results to those contained in [Sochaczewska, A.: <italic>The strong quasi-uniform convergence</italic>, Math. Montisnigri <bold>15 </bold>(2002), 45-55].</p></abstract>

Using ideals, we introduce a new class of topological spaces that are more general concept than R0 spaces [Cs´asz´ar, ´ A.: General Topology. Akad- ´emiai Kiad´o, Budapest, 1978]. Different properties will be studied for that class of topological spaces. We also define a new kind of convergence for sequences of functions and formulate more general results to those contained in [Sochaczewska, A.: The strong quasi-uniform convergence, Math. Montisnigri 15 (2002), 45-55].

On the ℑ-R<sub>0</sub> spaces and ℑ-strong quasi-uniform convergence

Institute of Mathematics Academia Pomeraniensis Arciszewskiego 22d 76-200 Słupsk POLAND

Tatra Mountains Mathematical Publications

On the ℑ-R spaces and ℑ-strong quasi-uniform convergence

Using ideals, we introduce a new class of topological spaces that are more general concept than R0 spaces [Cs´asz´ar, ´ A.: General Topology. Akad- ´emiai...

On the ℑ-R₀ spaces and ℑ-strong quasi-uniform convergence

Published Online: Nov 19, 2012

Page range: 29 - 45

DOI: https://doi.org/10.2478/v10127-012-0023-y

Keywords
quasi-strong convergence, ℑ-open covers, continuous function, ℑ-T<sub>3</sub> space, ℑ-R<sub>0</sub> space.

This content is open access.

On the ℑ-R0 spaces and ℑ-strong quasi-uniform convergence