A new form of -compactness is introduced in -topological spaces by -open -sets and their inequality where is a complete de Morgan algebra. It doesn’t rely on the structure of the basis lattice . It can also be characterized by means of -closed -sets and their inequality. When is a completely distributive de Morgan algebra, its many characterizations are presented and the relations between it and the other types of compactness are discussed. Countable -compactness and the -Lindelöf property...
In this paper, considering being a completely distributive lattice, we first introduce the concept of -fuzzy ideal degrees in an effect algebra , in symbol . Further, we characterize -fuzzy ideal degrees by cut sets. Then it is shown that an -fuzzy subset in is an -fuzzy ideal if and only if which can be seen as a generalization of fuzzy ideals. Later, we discuss the relations between -fuzzy ideals and cut sets (-nested sets and -nested sets). Finally, we obtain that the -fuzzy...
Based on a completely distributive lattice , degrees of compatible -subsets and compatible mappings are introduced in an -approximation space and their characterizations are given by four kinds of cut sets of -subsets and -equivalences, respectively. Besides, some characterizations of compatible mappings and compatible degrees of mappings are given by compatible -subsets and compatible degrees of -subsets. Finally, the notion of complete -sublattices is introduced and it is shown that the...
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