Some Issues On Topological Operators Via Ideals

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt,

2 Department of Physics and Engineering Mathematics, Faculty of Engineering, Kafrelsheikh University, Kafrelsheikh 33516, Egypt;

3 Department of Mathematics, Faculty of Science, new Valley University, Egypt.

Abstract

In a topological structure (X1,τ) any ideal I of a subset of X induces a new topology τ1 (I). If Y is a regular structure, then under some assumptions on I, for any upper τ∗- quasi continuous multivalued map F : X1 → P(Y )\∅ ,the sets of all points at which F is lower quasi- continuous (lower semi-continuous with respect to τ∗ or τ coincides). If F is compact- valued lower τ∗ - quasi continuous, then the symmetrical result holds (J.Ewert [8]). The paper concerns operators in ideal topological structures. Some properties and characterizations of the set operator ( )∗s are investigated and explored. We define, explore, and analyze nano semi- local function as well as some of its characteristics. Finally, we design a graph of vital places in our city with regard to ideals. 

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