Theory of Generalized Sets in Generalized Topological Spaces

Mohammad Irshad Khodabocus; Noor-ul-hacq Sookıa

doi:10.53570/jnt.896345

EN

Theory of Generalized Sets in Generalized Topological Spaces

Abstract

Several specific types of generalized sets (briefly, g-T_g-sets in generalized topological spaces (briefly, T_g-spaces have been defined and investigated for various purposes from time to time in the literature of T_g-spaces. Our recent research in the field of a new class of g-T_g-sets in T_g-spaces is reported herein as a starting point for more generalized classes. It is shown that the class of g-T_g-sets is a superclass of those whose elements are called open, closed, semi-open, semi-closed, pre-open, pre-closed, semi-pre-open, and semi-pre-closed sets in a T_g-space. A subclass of the T_g-subspace corresponds to the class of g-T_g-sets of a T_g-space. A class of g-T_g-sets of the Cartesian product of these T_g-spaces corresponds to the Cartesian product of a finite number of classes of g-T_g-sets, each of which belongs to a T_g-space. Diagrams establish the various relationships amongst the classes presented here and in the literature, and an ad hoc application supports the overall theory.

Keywords

Generalized topology, Generalized topological space, Generalized operations, Generalized open sets, Generalized closed sets

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Mohammad Irshad Khodabocus ^*
0000-0003-2252-4342
Mauritius

Noor-ul-hacq Sookıa
0000-0002-3155-0473
Mauritius

Publication Date

September 30, 2021

Submission Date

March 13, 2021

Acceptance Date

September 20, 2021

Published in Issue

Year 2021 Number: 36

DOI

https://doi.org/10.53570/jnt.896345

IZ

https://izlik.org/JA62SZ67EK

APA

Khodabocus, M. I., & Sookıa, N.- ul- hacq. (2021). Theory of Generalized Sets in Generalized Topological Spaces. Journal of New Theory, 36, 18-38. https://doi.org/10.53570/jnt.896345

AMA

1.Khodabocus MI, Sookıa N ul hacq. Theory of Generalized Sets in Generalized Topological Spaces. JNT. 2021;(36):18-38. doi:10.53570/jnt.896345

Chicago

Khodabocus, Mohammad Irshad, and Noor-ul-hacq Sookıa. 2021. “Theory of Generalized Sets in Generalized Topological Spaces”. Journal of New Theory, nos. 36: 18-38. https://doi.org/10.53570/jnt.896345.

EndNote

Khodabocus MI, Sookıa N- ul- hacq (September 1, 2021) Theory of Generalized Sets in Generalized Topological Spaces. Journal of New Theory 36 18–38.

IEEE

[1]M. I. Khodabocus and N.- ul- hacq Sookıa, “Theory of Generalized Sets in Generalized Topological Spaces”, JNT, no. 36, pp. 18–38, Sept. 2021, doi: 10.53570/jnt.896345.

ISNAD

Khodabocus, Mohammad Irshad - Sookıa, Noor-ul-hacq. “Theory of Generalized Sets in Generalized Topological Spaces”. Journal of New Theory. 36 (September 1, 2021): 18-38. https://doi.org/10.53570/jnt.896345.

JAMA

1.Khodabocus MI, Sookıa N- ul- hacq. Theory of Generalized Sets in Generalized Topological Spaces. JNT. 2021;:18–38.

MLA

Khodabocus, Mohammad Irshad, and Noor-ul-hacq Sookıa. “Theory of Generalized Sets in Generalized Topological Spaces”. Journal of New Theory, no. 36, Sept. 2021, pp. 18-38, doi:10.53570/jnt.896345.

Vancouver

1.Mohammad Irshad Khodabocus, Noor-ul-hacq Sookıa. Theory of Generalized Sets in Generalized Topological Spaces. JNT. 2021 Sep. 1;(36):18-3. doi:10.53570/jnt.896345