On Some Properties of R.D. Kopperman’s Stable Bitopological Spaces
by
Irakli Dochviri
Department of Applied Mathematics, Georgian Technical University, 0175 Tbilisi, 77 M.Kostava, Georgia

The asymmetric topology is one of the relatively new branches of modern mathematics. A central role in asymmetric topology play bitopologies, i.e. structures of the ordered pairs of topologies defined one and same sets. Usually, an ordered triple (X, t₁, t₂) is called to be bitopological space [1] . Nowadays bitopological reasons are useful for computer scince too. In this talk I present some of my results concerning to the stable bitopological spaces. Following to [2], a bitopological space (X, t₁, t₂) is called stable iff every nonempty closed set is compact relatively to the another topology. Using modified construction of A.Taimanov [3] we prove main result of this work. Recall that int the Theorem bellow is assumed that i, j ∈ {1;2} and i ≠ j . Moreover, a single valued map f:(X, t₁, t₂) → (Y, g₁, g₂) is called (i, j)-D continuous if f:(X, t_i) → (Y, g_j) is continuous. For other notions used in the theorem see e.g. [4].

THEOREM: Let a bispace (X, t₁, t₂) be an (i, j)-submaximal and (Y, g₁, g₂) be p-E.D., (i, j)-QHC, (i, j)-stable, j-Urysohn bispace. Suppose that for a set A ∈ d-D(X) a map

REFERENCES:

1. J.C. Kelly. Bitopological spaces // Proc. London Math Soc., 9(13) (1963), 71-89.

2. R.D. Kopperman. Assymetry and duality in topology // Topol. Appl., 66 (1995), 1-39.

3. A.D. Taimanov. On extension of continuous maps of topological spaces // Russ. Math. Sb., 31(73), (1952), 459-463.

4. I. Dochviri. On some properties of bitopological QHC spaces // Lithuanian Math. Journal, 46(2), 2006, 150-154.

Date received: April 30, 2008