On fixed edges of antitone self-mappings of complete lattices.
Fixed circle problems belong to a realm of problems in metric fixed point theory. Specifically, it is a problem of finding self mappings which remain invariant at each point of the circle in the space. Recently this problem is well studied in various metric spaces. Our present work is in the domain of the extension of this line of research in the context of fuzzy metric spaces. For our purpose, we first define the notions of a fixed circle and of a fixed Cassini curve then determine suitable conditions...
Four new operators, which are analogous of the topological operators interior and closure, are defined. Some of their basic properties are studied. Their geometrical interpretations are given.
We find all continuous iterative roots of nth order of a Sperner homeomorphism of the plane onto itself.
Following Kombarov we say that is -sequential, for , if for every non-closed subset of there is such that and . This suggests the following definition due to Comfort and Savchenko, independently: is a FU()-space if for every and every there is a function such that . It is not hard to see that ( denotes the Rudin–Keisler order) every -sequential space is -sequential every FU()-space is a FU()-space. We generalize the spaces to construct examples of -sequential...
We apply elementary substructures to characterize the space for Corson-compact spaces. As a result, we prove that a compact space is Corson-compact, if can be represented as a continuous image of a closed subspace of , where is compact and denotes the canonical Lindelöf space of cardinality with one non-isolated point. This answers a question of Archangelskij [2].