Certain new classes of generalized closed sets and their applications in ideal topological spaces

doi:10.2298/FIL1505113M

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Certain new classes of generalized closed sets and their applications in ideal topological spaces

Journal Article•DOI•

Certain new classes of generalized closed sets and their applications in ideal topological spaces

Dhananjoy Mandal¹, M. N. Mukherjee¹•Institutions (1)

University of Calcutta¹

30 Mar 2015-Filomat (National Library of Serbia)-Vol. 29, Iss: 5, pp 1113-1120

TL;DR: In this paper, a type of closed sets, called {star}-g-closed sets, is introduced and studied in an ideal topological space, which lies strictly between the class of all closed sets and that of generalized closed sets of Levine.

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Abstract: In this paper, a type of closed sets, called {star}-g-closed sets, is introduced and studied in an ideal topological space. The class of such sets is found to lie strictly between the class of all closed sets and that of generalized closed sets of Levine [1]. We give some applications of {star}-g-closed set and {star}-g-open set in connection with certain separation axioms.

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Journal Article•DOI•

On certain types of sets in ideal topological spaces

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Dhananjoy Mandal, M. N. Mukherjee

01 Jan 2015-Annals of the West University of Timisoara: Mathematics and Computer Science

TL;DR: In this article, the authors introduce some typical sets in an ideal topological space and prove several properties of the introduced classes of sets, and finally as application, they initiate the study of a kind of separation axiom, termed *−T12 $* -T_{{1 \\over 2}}$ -property.

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Abstract: Abstract In the present article we introduce certain typical sets in an ideal topological space, some such corresponding versions in topological spaces being already there in the literature. We prove several properties of the introduced classes of sets, and finally as application, we initiate the study of a kind of separation axiom, termed *−T12 $* - T_{{1 \\over 2}}$ -property.

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Cites background from "Certain new classes of generalized ..."

...Certain descriptions of such sets along with those in connection with the ∗-g-open and ∗-g-closed sets of [7] are incorporated in this section....
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...6 of [7] we have, cl(A)\A does not contain any nonempty ∗-closed set....
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...It was shown in [7] that the the class of ∗-g-closed sets lies strictly between the class of closed sets and the class of g-closed sets....
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...A subset A of an ideal space (X, τ, I) is said to be ∗-g-closed [7] if cl(A) ⊆ U whenever A ⊆ U and U is ∗-open....
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COMPLETELY g-ӿ-CLOSED SETS

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I. Rajasekaran, O. Nethaji

31 Dec 2020

TL;DR: In this article, the notion of completely g-completely g-/-closed set,-closed sets is introduced in ideal topological spaces and a characterization of normal spaces is given in terms of complete closed sets.

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Abstract: In this paper, the notion of completely g-completely g-/-closed set,-closed sets is introduced in ideal topological spaces. Characterizations and properties of completely g-?-closed sets and completely g-completely g-/-closed set,-open sets are given. A characterization of normal spaces is given in terms of completely g-completely g-/-closed set,-open sets. Also, it is established that a completely g-completely g-/-closed set,-closed subset of an I-compactspace is I-compact

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References

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Journal Article•DOI•

Generalized closed sets in topology

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Norman Levine

01 Jan 1970-Rendiconti Del Circolo Matematico Di Palermo

761 citations

Journal Article•DOI•

New topologies from old via ideals

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Dragan Jankovic¹, T. R. Hamlett¹•Institutions (1)

East Central University¹

01 Mar 1990-American Mathematical Monthly

TL;DR: In this paper, the authors present a new topology from old via Ideals, which they call New Topologies from Old through Ideals (New Topology from Old via IBE).

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Abstract: (1990). New Topologies from Old via Ideals. The American Mathematical Monthly: Vol. 97, No. 4, pp. 295-310.

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483 citations

Generalized α-Closed Sets in Topology

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春夫牧, R. Devi, Krishnan Balachandran

01 Jan 1993

377 citations

"Certain new classes of generalized ..." refers background in this paper

...The class of such sets is found to lie strictly between the class of all closed sets and that of generalized closed sets of Levine [5]....
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...A subset A of X is said to be 1-closed [5] if cl(A) ⊆ U whenever A ⊆ U and U is open in X; and the complement of a 1-closed subset in X is called a 1-open set in X....
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...In 1970, Levine [5] first introduced the novel idea of generalized closed (1-closed, for short) sets, a generalization of closed sets having their own meaningful facets....
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Journal Article•DOI•

The localisation theory in set-topology

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R. Vaidyanathaswamy

01 Jul 1944

205 citations

"Certain new classes of generalized ..." refers background in this paper

...The notion of ideals in general topological spaces is treated in the classic text by Kuratowski [4] and also in [10]....
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Journal Article•DOI•

Indexed Systems of Neighborhoods for General Topological Spaces

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A. S. Davis¹•Institutions (1)

University of Oklahoma¹

01 Nov 1961-American Mathematical Monthly

TL;DR: The Indexed Systems of Neighborhoods for General Topological Spaces (ISGNSS) as mentioned in this paper is a system for general topological spaces, which is based on the idea of topology.

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Abstract: (1961). Indexed Systems of Neighborhoods for General Topological Spaces. The American Mathematical Monthly: Vol. 68, No. 9, pp. 886-894.

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179 citations

"Certain new classes of generalized ..." refers background in this paper

...∗-R0-Space and I -R0-space The notion of R0-space, first introduced by Davis [1], has been studied by many topologists....
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...We begin with the following definition recalled from [1]....
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...The notion of R0-space, first introduced by Davis [1], has been studied by many topologists....
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