scholarly journals Contra-continuous functions and stronglyS-closed spaces

1996 ◽  
Vol 19 (2) ◽  
pp. 303-310 ◽  
Author(s):  
J. Dontchev
Keyword(s):  
Dense Subset ◽  
Continuous Functions ◽  
Closed Space ◽  
Closed Sets ◽  
Open Set ◽  
Locally Closed Sets ◽  
Continuous Images

In 1989 Ganster and Reilly [6] introduced and studied the notion ofLC-continuous functions via the concept of locally closed sets. In this paper we consider a stronger form ofLC-continuity called contra-continuity. We call a functionf:(X,τ)→(Y,σ)contra-continuous if the preimage of every open set is closed. A space(X,τ)is called stronglyS-closed if it has a finite dense subset or equivalently if every cover of(X,τ)by closed sets has a finite subcover. We prove that contra-continuous images of stronglyS-closed spaces are compact as well as that contra-continuous,β-continuous images ofS-closed spaces are also compact. We show that every stronglyS-closed space satisfies FCC and hence is nearly compact.

scholarly journals bT-Locally Closed Sets and bT-Locally Continuous Functions In Supra Topological Spaces.

2013 ◽  
Vol 6 (4) ◽  
pp. 18-22 ◽  
Author(s):  
K.Krishnaveni K.Krishnaveni
Keyword(s):  
Continuous Functions ◽  
Topological Spaces ◽  
Closed Sets ◽  
Locally Closed Sets

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

2021 ◽  
Vol 12 (3) ◽  
pp. 3444-3454
Author(s):  
Vijayakumari T Et.al
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Closed Set ◽  
Closed Sets ◽  
Open Set ◽  
Continuous Maps ◽  
Locally Closed Sets

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.

scholarly journals A decomposition of pairwise continuity via ideals

2016 ◽  
Vol 34 (1) ◽  
pp. 141-149
Author(s):  
T. Noiri ◽  
M. Rajamani ◽  
M. Maheswari
Keyword(s):  
Continuous Functions ◽  
Closed Sets ◽  
Bitopological Spaces ◽  
Locally Closed Sets

In this paper, we introduce and study the notions of (i, j) - regular - ℐ -closed sets, (i, j) - Aℐ -sets, (i, j) - ℐ -locally closed sets, p- Aℐ -continuous functions and p- ℐ -LC-continuous functions in ideal bitopological spaces and investigate some of their properties. Also, a new decomposition of pairwise continuity is obtained using these sets.

Strongly minimal generalized locally closed sets and locally continuous functions

2014 ◽  
Vol 8 ◽  
pp. 2645-2654
Author(s):  
E. Subha ◽  
N. Nagaveni
Keyword(s):  
Continuous Functions ◽  
Closed Sets ◽  
Locally Closed Sets

scholarly journals Locally gωα-Closed Sets in Topological Spaces

2017 ◽  
Vol 19 ◽  
pp. 1-9
Author(s):  
S.S. Benchalli ◽  
Prakash Gouda Patil ◽  
Pushpa M. Nalwad
Keyword(s):  
Continuous Functions ◽  
Topological Spaces ◽  
Closed Sets ◽  
New Class ◽  
Locally Closed Sets

In the year 2014, the present authors introduced and studied the concept of gωα-closed sets in topological spaces. The purpose of this paper to introduce a new class of locally closed sets called gωα-locally closed sets (briefly gωαlc-sets) and study some of their properties. Also gωα-locally closed continuous (briefly gωαlc-continuous) functions and its irresolute functions are introduced and studied their properties in topological spaces.

Novel Idea of Gδ-α-Locally Continuous Functions

2021 ◽  
pp. 61-65
Author(s):  
R.Narmada Devi ◽  
Keyword(s):  
Continuous Function ◽  
Compact Space ◽  
Continuous Functions ◽  
Connected Space ◽  
Urysohn Space ◽  
Closed Sets ◽  
New Concepts ◽  
Locally Closed Sets

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.

scholarly journals Locally closed sets andLC-continuous functions

1989 ◽  
Vol 12 (3) ◽  
pp. 417-424 ◽  
Author(s):  
M. Ganster ◽  
I. L. Reilly
Keyword(s):  
Topological Space ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Closed Set ◽  
Closed Sets ◽  
Generalized Continuity ◽  
Locally Closed Sets ◽  
Nearly Continuous

In this paper we introduce and study three different notions of generalized continuity, namely LC-irresoluteness, LC-continuity and sub-LC-continuity. All three notions are defined by using the concept of a locally closed set. A subset S of a topological space X is locally closed if it is the intersection of an open and a closed set. We discuss some properties of these functions and show that a function between topological spaces is continuous if and only if it is sub-LC-continuous and nearly continuous in the sense of Ptak. Several examples are provided to illustrate the behavior of these new classes of functions.

ON A NEW CLASS OF SEMI GENERALIZED CLOSED SETS IN STRONG GENERALIZED TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (11) ◽  
pp. 9353-9360
Author(s):  
G. Selvi ◽  
I. Rajasekaran
Keyword(s):  
Topological Spaces ◽  
Closed Set ◽  
Basic Properties ◽  
Closed Sets ◽  
New Class ◽  
Open Set ◽  
Continuous Maps

This paper deals with the concepts of semi generalized closed sets in strong generalized topological spaces such as $sg^{\star \star}_\mu$-closed set, $sg^{\star \star}_\mu$-open set, $g^{\star \star}_\mu$-closed set, $g^{\star \star}_\mu$-open set and studied some of its basic properties included with $sg^{\star \star}_\mu$-continuous maps, $sg^{\star \star}_\mu$-irresolute maps and $T_\frac{1}{2}$-space in strong generalized topological spaces.

Sign in / Sign up

Export Citation Format

Share Document