Version 1
: Received: 21 March 2020 / Approved: 23 March 2020 / Online: 23 March 2020 (07:14:43 CET)
How to cite:
Khodabocus, M. I.; Sookia, N.-U.-H. Theory of g-Tg-Exterior and g-Tg-Frontier Operators: Definitions, Essential Properties and, Consistent, Independent Axioms. Preprints2020, 2020030342. https://doi.org/10.20944/preprints202003.0342.v1
Khodabocus, M. I.; Sookia, N.-U.-H. Theory of g-Tg-Exterior and g-Tg-Frontier Operators: Definitions, Essential Properties and, Consistent, Independent Axioms. Preprints 2020, 2020030342. https://doi.org/10.20944/preprints202003.0342.v1
Khodabocus, M. I.; Sookia, N.-U.-H. Theory of g-Tg-Exterior and g-Tg-Frontier Operators: Definitions, Essential Properties and, Consistent, Independent Axioms. Preprints2020, 2020030342. https://doi.org/10.20944/preprints202003.0342.v1
APA Style
Khodabocus, M. I., & Sookia, N. U. H. (2020). Theory of g-Tg-Exterior and g-Tg-Frontier Operators: Definitions, Essential Properties and, Consistent, Independent Axioms. Preprints. https://doi.org/10.20944/preprints202003.0342.v1
Chicago/Turabian Style
Khodabocus, M. I. and Noor-Ul-Hacq Sookia. 2020 "Theory of g-Tg-Exterior and g-Tg-Frontier Operators: Definitions, Essential Properties and, Consistent, Independent Axioms" Preprints. https://doi.org/10.20944/preprints202003.0342.v1
Abstract
In a generalized topological space Tg = (Ω, Tg), generalized interior and generalized closure operators g-Intg, g-Clg : P (Ω) −→ P (Ω), respectively, are merely two of a number of generalized primitive operators which may be employed to topologize the underlying set Ω in the generalized sense. Generalized exterior and generalized frontier operators g-Extg, g-Frg : P (Ω) −→ P (Ω), respectively, are other generalized primitive operators by means of which characterizations of generalized operations under g-Intg, g-Clg : P (Ω) −→ P (Ω) can be given without even realizing generalized interior and generalized closure operations first in order to topologize Ω in the generalized sense. In a recent work, the present authors have defined novel types of generalized interior and generalized closure operators g-Intg, g-Clg : P (Ω) −→ P (Ω), respectively, in Tg and studied their essential properties and commutativity. In this work, they propose to present novel definitions of generalized exterior and generalized frontier operators g-Extg, g-Frg : P (Ω) −→ P (Ω), respectively, a set of consistent, independent axioms after studying their essential properties, and established further characterizations of generalized operations under g-Intg, g-Clg : P (Ω) −→ P (Ω) in Tg.
Computer Science and Mathematics, Geometry and Topology
Copyright:
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