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.

It is that the all δ-open sets are open sets,all open sets are α-open sets,α-open sets are semi-open sets and preopen sets,semi-open sets or preopen sets are β-open sets.

In this paper, we introduced concepts on semi-arcwise connected space and semi-arcwise connection by the concepts of semi-open sets and semi-continuous mapping, pobularized the concepts on arcwise connected spaces.

On this paper,we introduced concepts on \$s\$-arc connected space and \$s\$-arc connected by the theory of semi-open sets.

Strong Semi-open Sets in Fuzzifying Spaces;

The notions of preopen sets and pre-semiopen sets are firstly discussed in L-topological spaces.

In this paper,concepts of Pre-semiopen sets,Sub-strong semiopen sets and Strong semiopen sets were introduced in topological space in a new way,and their relations and properties were discussed.