Abstract
A new form of β-compactness is introduced in L-topological spaces by means of β-open L-sets and their inequality where L is a complete de Morgan algebra. This new form doesn’t rely on the structure of basis lattice L. It can also be characterized by means of β-closed L-sets and their inequality. When L is a completely distributive de Morgan algebra, its many characterizations are presented. Meanwhile countable β-compactness and the β-Lindel¨of property are also researched.
Highlights
As we know, stronger and weaker forms of compactness occupy very important places in general topology
In [5], Abd El-Monsef et al introduced the concepts of β-open sets and β-continuous functions in general topology, and Fath Alla in [1] introduced these concepts in [0,1]-topological spaces
In [12, 13], a new definition of fuzzy compactness is presented in Ltopological spaces by means of open L-sets and their inequality where L is a complete de Morgan algebra
Summary
Stronger and weaker forms of compactness occupy very important places in general topology. In [12, 13], a new definition of fuzzy compactness is presented in Ltopological spaces by means of open L-sets and their inequality where L is a complete de Morgan algebra. In this paper, following the lines of [12, 13], we shall introduce a new form of β-compactness in L-topological spaces by means of β-open L-sets and their inequality. This new form of β-compactness has many characterizations if L is completely distributive
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