The aim of this paper is to introduce and study gp-continuous maps. Basic characterizations and several properties concerning them are obtained.Further,gp-irresolute map is also defined. Some of the properties are investigated. 1991 AMS Classification: 54A05, 54D10.

In this paper, we introduce the concepts of fuzzy pairwise (r, s)-irresolute, fuzzy pairwise (r, s)-presemiopen and fuzzy pairwise (r, s)-presemiclosed mappings in smooth bitopological spaces and then we investigate some of their characteristic properties.

Parallel to the concept of quasi-separate continuity, we define a notion for quasi-oscillation of a mapping f : X × Y → R. We also introduce a topological game on X to approximate the oscillation of f . It follows that under suitable conditions, every quasi-separately continuous mapping f : X×Y → R has the Namioka property. An illuminating example is also given.

We investigate a dense subgroup Γ of the second Morava stabilizer group given by a certain group of quasi-isogenies of a supersingular elliptic curve in characteristic p. The group Γ acts on the Bruhat-Tits building for GL2(Q`) through its action on the `-adic Tate module. This action has finite stabilizers, giving a small resolution for the homotopy fixed point spectrum (EhΓ 2 ) hGal by spectr...

The appropriate general completeness notion for topological vector spaces is quasi-completeness. There is a stronger general notion of completeness, which proves to be too strong in general. For example, the appendix shows that weak-star duals of infinite-dimensional Hilbert spaces are quasi-complete, but never complete in the stronger sense. Quasi-completeness for Fréchet spaces is ordinary me...

Building upon work of Y. Shalom we give a homological-algebra flavored definition of an induction map in group homology associated to a topological coupling. As an application we obtain that the cohomological dimension cdR over a commutative ring R satisfies the inequality cdR(Λ) ≤ cdR(Γ) if Λ embeds uniformly into Γ and cdR(Λ) < ∞ holds. Another consequence of our results is that the Hirsch ra...