Regular Gδ-diagonal and mappings

Completely Regular Mappings and Dimension

Regular Mappings between Dimensions

The notions of Lipschitz and bilipschitz mappings provide classes of mappings connected to the geometry of metric spaces in certain ways. A notion between these two is given by “regular mappings” (reviewed in Section 1), in which some non-bilipschitz behavior is allowed, but with limitations on this, and in a quantitative way. In this paper we look at a class of mappings called (s, t)-regular m...

Fuzzy $e$-regular spaces and strongly $e$-irresolute mappings

The aim of this paper is to introduce fuzzy ($e$, almost) $e^{*}$-regular spaces in $check{S}$ostak's fuzzy topological spaces. Using the $r$-fuzzy $e$-closed sets, we define $r$-($r$-$theta$-, $r$-$etheta$-) $e$-cluster points and their properties. Moreover, we investigate the relations among $r$-($r$-$theta$-, $r$-$etheta$-) $e$-cluster points, $r$-fuzzy ($e$, almost) $e^{*}$-regular spaces a...

Mappings preserving regular hexahedrons

for all x, y ∈ X . A distance r > 0 is said to be preserved (conservative) by a mapping f : X → Y if ‖ f (x)− f (y)‖ = r for all x, y ∈ X with ‖x− y‖ = r. If f is an isometry, then every distance r > 0 is conservative by f , and conversely. We can now raise a question whether each mapping that preserves certain distances is an isometry. Indeed, Aleksandrov [1] had raised a question whether a ma...

Generalized Regular Fuzzy Irresolute Mappings and Their Applications

In this paper, the notion of generalized regular fuzzy irresolute, generalized regular fuzzy irresolute open  and generalized regular fuzzy irresolute closed maps in fuzzy  topological spaces are introduced and studied. Moreover, some separation axioms and $r$-GRF-separated sets are established. Also, the relations between generalized regular fuzzy continuous maps and generalized regular fuzzy ...