**B. Dvalishvili**

## Connectedness of a Fine Topology and Localization
in Bitopological Spaces

**Abstract:**

The paper, consisting of four sections, of which Section 0 is auxiliary, is
devoted to some principal questions of the theory of bitoplogical spaces. In
Section 1, the p-extremally disconnected, (i,j)-strongly extremally disconnected
and (i,j)-nodec spaces are studied by means of the localization at a point. In
Section 2, the (i,j)-pseudoscattered, (i,j)-nd-scattered, p-ultradisconnected
and (i,j)-Moscow spaces are introduced, their interrelations and their relations
with the p-extremally disconnected spaces are investigated, in particular, when
one of the topologies is finer than the other. Section 3 is concerned with the
problem of existence of a finer connected topology on a connected topological
space and so, it is related to the concept of a maximal connected space.

**Keywords:**

C-, N- and D-relations; (i,j)-Baire space in the strong sense, WS-tangency and
weak tangency of topologies, (i,j)-strongly disconnected, p-ultradisconnected,
p-crowded, (i,j)-nodec, (i,j)-nd-scattered, (i,j)-pseudoscattered and (i,j)-Moscow
spaces, point of i,j)-(strong)-extremal disconnectedness, (i,j)-nodec and (i,j)-P-points.

**MSC 2000:** 54E55