Open set and closed aggregate in Function of Read VariaNe;

This paper studies the composition of the open sets in Rn spaces and obtains the theorem of the composition of the open sets in Rn spaces.

In point set topological theory, open set and neighborhood are the basic concept.

Definition of the a-open set and the a-closed set in LF-topological spaces given,efforts are made to define the a- connectedness by means of a-open sets,following which a probe into some of its basic properties and equivalent depiction is done as well.

In the first part, the author introducesthe new notion of b-I-open sets in the ideal topological spaces and uses b-I-open sets to define b-I-continuous mappings and b-I-compact (b-I-paracompact) spaces.

Based on the literatures,the properties of SH-connectedness in the topological spaces were discussed by using the properties of semi-open sets of the semi-topological spaces.

Mian results : If X is a S-cmpactness space, and X has finite semi-open set interrec- tion property then(1)If X is a S_2-space, then X is a S_3 *-space; (2)If X is a S_2-space, then X is a S_4 *- space; (3) If X is a S_3 * -space, then X is a S_4 * -space.

Further more the relationship of q-open sets to semi-open sets and pre-open sets are discussed.

Three new spaces on operator open set theory;

This paper discusses the T-Lindelf space and explores the nature of its subspace in operator open set theory.

In this paper, the definitions were given of operator compact space, operator countably compact space and operator Lindelof space in operator open set theory.