In this paper we introduce the concept of -closed sets and investigate some of its properties in the spaces considered by A. D. Alexandroff [1] where only countable unions of open sets are required to be open. We also introduce a new separation axiom called -axiom in the Alexandroff spaces with the help of -closed sets and investigate some of its consequences.
In this paper, we prove that a space is a -metrizable space if and only if is a weak-open, and -image of a semi-metric space, if and only if is a strong sequence-covering, quotient, and -image of a semi-metric space, where “semi-metric” can not be replaced by “metric”.
Given a space , its -subsets form a basis of a new space , called the -modification of . We study how the assumption that the -modification is homogeneous influences properties of . If is first countable, then is discrete and, hence, homogeneous. Thus, is much more often homogeneous than itself. We prove that if is a compact Hausdorff space of countable tightness such that the -modification of is homogeneous, then the weight of does not exceed (Theorem 1). We also establish...
-separation axioms are introduced in ordered fuzzy topological spaces and some of their basic properties are investigated besides establishing an analogue of Urysohn’s lemma.
Let G be a compact group and X a G-ANR. Then X is a G-AR iff the H-fixed point set is homotopy trivial for each closed subgroup H ⊂ G.
In this paper fixed point theorems for maps with nonempty convex values and having the local intersection property are given. As applications several minimax inequalities are obtained.