Quasihomeomorphisms and Skula spaces

Let [Formula: see text] be a topological space. By the Skula topology (or the [Formula: see text]-topology) on [Formula: see text], we mean the topology [Formula: see text] on [Formula: see text] with basis the collection of all [Formula: see text]-locally closed sets of [Formula: see text], the resulting space [Formula: see text] will be denoted by [Formula: see text]. We show that the following results hold: (1) [Formula: see text] is an Alexandroff space if and only if the [Formula: see text]-reflection [Formula: see text] of [Formula: see text] is a [Formula: see text]-space. (2) [Formula: see text] is a Noetherian space if and only if [Formula: see text] is finite. (3) If we denote by [Formula: see text] the Alexandroff extension of [Formula: see text], then [Formula: see text] if and only if [Formula: see text] is a Noetherian quasisober space. We also give an alternative proof of a result due to Simmons concerning the iterated Skula spaces, namely, [Formula: see text]. A space is said to be clopen if its open sets are also closed. In [R. E. Hoffmann, Irreducible filters and sober spaces, Manuscripta Math. 22 (1977) 365–380], Hoffmann introduced a refinement clopen topology [Formula: see text] of [Formula: see text]: The indiscrete components of [Formula: see text] are of the form [Formula: see text], where [Formula: see text] and [Formula: see text] is the intersection of all open sets of [Formula: see text] containing [Formula: see text] (equivalently, [Formula: see text]). We show that [Formula: see text]

SGP- LOCALLY CLOSED SETS IN TOPOLOGICAL SPACES (PART -II)

The aim of this paper is to introduce the new class of sgp- locally closed sets in topological spaces and studied some of their properties and characterizations.

Relations of Pre Generalized Regular Weakly Locally Closed Sets in Topological Spaces

In this paper pgrw-locally closed set, pgrw-locally closed*-set and pgrw-locally closed**-set are introduced. A subset A of a topological space (X,t) is called pgrw-locally closed (pgrw-lc) if A=GÇF where G is a pgrw-open set and F is a pgrw-closed set in (X,t). A subset A of a topological space (X,t) is a pgrw-lc* set if there exist a pgrw-open set G and a closed set F in X such that A= GÇF. A subset A of a topological space (X,t) is a pgrw-lc**-set if there exists an open set G and a pgrw-closed set F such that A=GÇF. The results regarding pgrw-locally closed sets, pgrw-locally closed* sets, pgrw-locally closed** sets, pgrw-lc-continuous maps and pgrw-lc-irresolute maps and some of the properties of these sets and their relation with other lc-sets are established.

Novel Idea of Gδ-α-Locally Continuous Functions

The new concepts of a neutrosophic Gδ set and neutrosophic Gδ-α-locally closed sets are introduced. Also, a neutrosophic εGδ-α-locally quasi neighborhood, neutrosophic Gδ-α-locally continuous function, neutrosophic Gδ-α-local T2 space, neutrosophic Gδ-α-local Urysohn space, neutrosophic Gδ-α-local connected space, and neutrosophic Gδ-α-local compact space are discussed and some interesting properties are established.

Study of RL-Connectedness and RL-Compactness

In this paper, we introduce a new kind of locally closed sets called regular locally closed sets (brie y RL-closed sets) in a topological space which are weaker than the locally closed sets. Regular locally continuous maps and regular locally irresolute maps are also introduced and studied some of their properties. Finally, we introduce the concept of regular locally connectedness and regular locally compactness on a topological space using the RL-closed sets.

Nano M Locally Closed Sets and Maps in Nano Topological Spaces

The concepts of sets, continuous and irresolute functions are introduced some of its characteristics are discussed. Also nano submaximal spaces are defined its properties are discussed.