scholarly journals Some generalization of (1,2)SP-locally closed sets in bitopological spaces

2021 ◽  
Keyword(s):  
Closed Sets ◽  
Bitopological Spaces ◽  
Locally Closed Sets

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 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 Generalized ψ∗-closed sets in bitopological spaces

2015 ◽  
Vol 23 (3) ◽  
pp. 527-534 ◽  
Author(s):  
H.M. Abu Donia ◽  
M.A. Abd Allah ◽  
A.S. Nawar
Keyword(s):  
Closed Sets ◽  
Bitopological Spaces

Quasihomeomorphisms and Skula spaces

2021 ◽  
Author(s):  
Othman Echi
Keyword(s):  
Topological Space ◽  
Alternative Proof ◽  
Manuscripta Math ◽  
Alexandroff Space ◽  
Closed Sets ◽  
Locally Closed Sets ◽  
Reflection Formula

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]

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 On semi star generalized closed sets in bitopological spaces

2010 ◽  
Vol 28 (1) ◽  
Author(s):  
K Chandrasekhara Rao ◽  
K. Kannan ◽  
D. Narasimhan
Keyword(s):  
Closed Sets ◽  
Bitopological Spaces
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