Resolvable maps preserve complete metrizability

Resolvable Maps Preserve Complete Metrizability

Let X be a Polish space, Y a separable metrizable space, and f : X → Y a continuous surjection. We prove that if the image under f of every open set or every closed set is resolvable, then Y is Polish. This generalizes similar results by Sierpiński, Vainštain, and Ostrovsky.

Quasimöbius maps preserve uniform domains

We show that if a domain Ω in a geodesic metric space is quasimöbius to a uniform domain in some metric space, then Ω is also uniform. Mathematics Subject Classification (2000). 30C65

Superstability of $m$-additive maps on complete non--Archimedean spaces

The stability problem of the functional equation was conjectured by Ulam and was solved by Hyers in the case of additive mapping. Baker et al. investigated the superstability of the functional equation from a vector space to real numbers. In this paper, we exhibit the superstability of $m$-additive maps on complete non--Archimedean spaces via a fixed point method raised by Diaz and Margolis.

Periodic Maps Which Preserve a Complex Structure

Almost resolvable minimum coverings of complete graphs with 4-cycles

If the complete graph Kn has vertex set X, a minimum covering of Kn with 4-cycles, (X,C, P ), is a partition of the edges of Kn ∪ P into a collection C of 4-cycles, where P is a subgraph of λKn and the number of edges in P is as small as possible. An almost parallel class of a minimum covering of Kn with 4-cycles is a largest possible collection of vertex disjoint 4-cycles (so with n/4 4-cycles...