On generalized preclosed sets, generalized precontinuous functions and Tgp-spaces in bitopological spaces.
by
Alias B. Khalaf
Dohuk University

The aim of the paper is to introduce generalized preclosed sets in bitopological spaces. If (X, t₁, t₂) is a bitopological space, a subset A of X is said to be (t_i, t_j)-gp-closed if t_j-_pCl A is a subset of G whenever A is a subset of G and G is t_j-open. Using such sets we define and study generalized precontinuous functions in bitopological spaces. We also study (t_i, t_j)-T_gp-spaces and strongly T_gp-spaces, where a bitopological space (X, t₁, t₂) is called a (t_i, t_j)-T_gp-space if every (t_i, t_j)-gp-closed set is t_j-closed, while it is called a strongly pairwise T_gp-space if it is a (t₁, t₂)-T_gp-space and a (t₂, t₁)-T_gp-space.

Finally we prove that in topological spaces the concepts of generalized preclosed and weakly generalized closed sets are equivalent.

Date received: May 3, 2001