scholarly journals On quasi I-openness and quasi I-continuity

2000 ◽  
Vol 31 (2) ◽  
pp. 101-108
Author(s):  
M. E. Abd El-Monsef ◽  
R. A. Mahmoud ◽  
A. A. Nasef
Keyword(s):  
Continuous Functions ◽  
Finite Additivity ◽  
Topological Properties ◽  
Closed Sets ◽  
New Concepts

A space $ (X,\tau,I)$ consisting of a nonempty set $ X$ with a topology $ \tau$ and an ideal $ I$ of subsets of $ X$ which has heredity and finite additivity properties. In this paper the quasi $ I$-open and quasi $ I$-closed sets are presented. Utilizing these new concepts the class of quasi $ I$-continuous functions have been obtained. Both of quasi $ I$-openness and quasi $ I$-continuity is considered as a generalization of those $ I$-openness and $ I$-continuity. However, numerous topological properties of these new notions have been discussed as well as many of their known results have been improved.

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 New approach of ideal topological generalized closed sets

2013 ◽  
Vol 31 (2) ◽  
pp. 191
Author(s):  
Chinnapazham Santhini ◽  
M. Lellis Thivagar
Keyword(s):  
Continuous Functions ◽  
New Approach ◽  
Closed Sets ◽  
New Class

In this paper,we introduce and investigate the notions of Iˆω -closed sets andI ˆω -continuous functions,maximal Iˆω -closed sets and maximal Iˆω -continuous functionsin ideal topological spaces.We also introduce a new class of spaces calledMTˆω -spaces.

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.

On locally δ-generalized closed sets and LδGC-continuous functions

2004 ◽  
Vol 19 (4) ◽  
pp. 995-1002 ◽  
Author(s):  
Jin Keun Park ◽  
Jin Han Park ◽  
Bu Young Lee
Keyword(s):  
Continuous Functions ◽  
Closed Sets

scholarly journals On generalizations of C*-embedding for wallman rings

1978 ◽  
Vol 25 (2) ◽  
pp. 215-229 ◽  
Author(s):  
H. L. Bentley ◽  
B. J. Taylor
Keyword(s):  
Topological Space ◽  
Continuous Functions ◽  
Topological Properties ◽  
Zero Sets ◽  
Algebraic Properties

AbstractBiles (1970) has called a subring A of the ring C(X), of all real valued continuous functions on a topological space X, a Wallman ring on X whenever Z(A), the zero sets of functions belonging to A, forms a normal base on X in the sense of Frink (1964). Previously, we have related algebraic properties of a Wallman ring A to topological properties of the Wallman compactification w(Z(A)) of X determined by the normal base Z(A). Here we introduce two different generalizations of the concept of “a C*-embedded subset” and study relationships between these and topological (respectively, algebraic) properties of w(Z(A)) (respectively, A).

scholarly journals Local invertibility in subrings of C*(X)

1992 ◽  
Vol 46 (3) ◽  
pp. 449-458 ◽  
Author(s):  
H. Linda Byun ◽  
Lothar Redlin ◽  
Saleem Watson
Keyword(s):  
Continuous Functions ◽  
Closed Sets ◽  
Complete Ring ◽  
Maximal Ideals ◽  
One To One ◽  
Local Invertibility ◽  
Bounded Continuous Functions ◽  
Ring Of Functions ◽  
Uniformly Closed

It is known that the maximal ideals in the rings C(X) and C*(X) of continuous and bounded continuous functions on X, respectively, are in one-to-one correspondence with βX. We have shown previously that the same is true for any ring A(X) between C(X) and C*(X). Here we consider the problem for rings A(X) contained in C*(X) which are complete rings of functions (that is, they contain the constants, separate points and closed sets, and are uniformly closed). For every noninvertible f ∈ A(X), we define a z–filter ZA(f) on X which, in a sense, provides a measure of where f is ‘locally invertible’. We show that the map ZA generates a correspondence between ideals of A(X) and z–filters on X. Using this correspondence, we construct a unique compactification of X for every complete ring of functions. Each such compactification is explicitly identified as a quotient of βX. In fact, every compactification of X arises from some complete ring of functions A(X) via this construction. We also describe the intersections of the free ideals and of the free maximal ideals in complete rings of functions.

scholarly journals A note on some applications ofα-open sets

2003 ◽  
Vol 2003 (2) ◽  
pp. 125-130 ◽  
Author(s):  
Miguel Caldas
Keyword(s):  
Continuous Functions ◽  
Topological Properties

The object of this note is to introduce and study topological properties ofα-derived,α-border,α-frontier, andα-exterior of a set using the concept ofα-open sets. Moreover, we study some further properties of the well-known notions ofα-closure andα-interior. We also obtain a new decomposition ofα-continuous functions.

scholarly journals Fine Fuzzy sp Closed Sets in Fine Fuzzy Topological Spaces

2020 ◽  
Vol 9 (3) ◽  
pp. 1306-1313
Keyword(s):  
Continuous Function ◽  
Topological Space ◽  
Inverse Image ◽  
Continuous Functions ◽  
Topological Spaces ◽  
The Novel ◽  
Closed Set ◽  
Closed Sets ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces

The main view of this article is the extended version of the fine topological space to the novel kind of space say fine fuzzy topological space which is developed by the notion called collection of quasi coincident of fuzzy sets. In this connection, fine fuzzy closed sets are introduced and studied some features on it. Further, the relationship between fine fuzzy closed sets with certain types of fine fuzzy closed sets are investigated and their converses need not be true are elucidated with necessary examples. Fine fuzzy continuous function is defined as the inverse image of fine fuzzy closed set is fine fuzzy closed and its interrelations with other types of fine fuzzy continuous functions are obtained. The reverse implication need not be true is proven with examples. Finally, the applications of fine fuzzy continuous function are explained by using the composition.

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