On \(\omega\)-almost-regularity and \(\omega\)-semi-regularity in topological spaces
Authors
S. Al Ghour
- Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan.
Abstract
In this paper, we give many characterizations of \(\omega \)%
-almost-regular topological spaces and show that \(\omega \)-almost-regularity
lies strictly between regularity and almost-regularity. Also, we give
several sufficient conditions for the equivalence between "\(\omega \)%
-almost-regularity" and "regularity", and between "\(\omega \)%
-almost-regularity" and "almost-regularity." Moreover, we show that \(\omega \)%
-almost-regularity is hereditary for certain classes of subspaces.
Furthermore, we show that the product of two\textbf{\ }\(\omega \)%
-almost-regular topological spaces is \(\omega \)-almost-regular. In addition
to these, we define \(\omega \)-semi-regularity as a new topological property.
With the help of examples, we study several relationships regarding \(\omega \)%
-semi-regularity, in particular, we show that \(\omega \)-semi-regularity is
strictly weaker than each of \(\omega \)-regularity and semi-regularity and
that \(\omega \)-regular Hausdorff topological spaces are \(\omega \)-Urysohn.
Share and Cite
ISRP Style
S. Al Ghour, On \(\omega\)-almost-regularity and \(\omega\)-semi-regularity in topological spaces, Journal of Mathematics and Computer Science, 31 (2023), no. 2, 188--196
AMA Style
Al Ghour S., On \(\omega\)-almost-regularity and \(\omega\)-semi-regularity in topological spaces. J Math Comput SCI-JM. (2023); 31(2):188--196
Chicago/Turabian Style
Al Ghour, S.. "On \(\omega\)-almost-regularity and \(\omega\)-semi-regularity in topological spaces." Journal of Mathematics and Computer Science, 31, no. 2 (2023): 188--196
Keywords
- \(\omega \)-openness
- \(R\omega \)-openness
- regularity
- almost regularity
- \(\omega \)-regularity
- semi-regularity
MSC
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