We introduce some local properties by soft semi-open sets. For example, soft semi-neighborhoods of the soft point, soft semi-first-countable spaces and soft semi-

Soft set theory [

In the recent years, papers about soft sets theory and their applications in various fields have been writing increasingly [

In the present study, we introduce some local properties by soft semi-open sets. For example, soft semi-neighborhoods of the soft point, soft semi-first-countable spaces, and soft semi-

Let

A pair

Let

A soft set

A soft set

The union of two soft sets

We write

The intersection of two soft sets of

Now we recall some definitions and results defined and discussed in [

For a soft set

Let

The union of any number of soft sets in

The intersection of any two soft sets in

The triplet

Let

Let

Let

Let

The soft interior of

The soft closure of

By property 2 for soft open sets,

By property 2 for soft closed sets,

Let

A soft set

A soft set

Let

The soft semi-interior of

The soft semi-closure of

A soft set

The semi-neighborhood system of a soft point

The semi-neighborhood system

(a) If

(b) If

(c) If

Let

Let

These properties are easily verified by referring to the corresponding properties of soft seminbds in Proposition

Let

Let

Let

Let

(a), (c) are obvious by definitions.

(b) For

Let

By the definition of soft semi-interior and Proposition

A soft set

Let

Let the sequence

Let the sequence

Let

(a)

(b) Let

In this part, we define the soft semi-

Let

Let

From Definition

Let

(a)

(b)

(b)

(c)

Let

(a)

(b)

(c)

(d)

Let

(a)

To prove that (b)

To prove that (c)

To complete (d)

Let

A soft topological space

Let

Because

Let

Suppose

A soft topological space

A soft topological space

By Theorem

Let

Suppose that

In this paper, we introduce the concept of soft semi-neighborhoods of the soft point, soft semi-

This work described here is supported by the Grants from the National Natural Science Foundation of China (NSFC no. 10971186, 11061004, 71140004, 61070241, 11226265), the Natural Scientific Foundation of Shandong Province (ZR2010AM019, ZR2010FM035, ZR2011AQ015, ZR2010AQ012, and 2012BSB01159). This work is also supported by the international cooperation in training projects for outstanding young teachers of higher institutions of Shandong Province. The author is grateful to the anonymous referees for careful checking of the details and for helpful comments that improved this paper.