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.

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.

FEEBLY GENERALIZED LOCALLY CLOSED SETS IN BITOPOLOGICAL SPACES

2020 ◽  
Vol 9 (5) ◽  
pp. 2497-2507
Author(s):  
S. V. Vani ◽  
K. Bala Deepa Arasi ◽  
S. Jackson
Keyword(s):  
Closed Sets ◽  
Bitopological Spaces ◽  
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.

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