scholarly journals Intuitionistic fuzzy based regular and normal spaces

2020 ◽  
Vol 26 (4) ◽  
pp. 53-63
Author(s):  
Tamanna Tasnim Prova ◽  
◽  
Md. Sahadat Hossain ◽  
Keyword(s):  
Normal Space ◽  
Regular Space ◽  
Topological Properties ◽  
Intuitionistic Fuzzy

In this paper, we define the notion of intuitionistic fuzzy based regular and normal spaces. We also study that classical regular and normal spaces are also intuitionistic fuzzy based regular and normal spaces but the converses are not true in general. This notion opens up a new conception of generalization of classical regular and normal spaces. The hereditary and topological properties of intuitionistic fuzzy based regular and normal spaces have been also investigated. Moreover, by setting some examples we show that every intuitionistic fuzzy based regular space as well as intuitionistic fuzzy based normal space need not be T1 spaces. Finally, it is shown that under some conditions the images and homeomorphic images are preserved in intuitionistic fuzzy based regular and normal spaces.

scholarly journals Intuitionistic Fuzzy Topological Spaces Model

2020 ◽  
Vol 55 (2) ◽  
Author(s):  
Hind Fadhil Abbas
Keyword(s):  
Hausdorff Space ◽  
Basic Structure ◽  
Normal Space ◽  
Regular Space ◽  
Topological Spaces ◽  
Intuitionistic Fuzzy ◽  
Separation Axioms ◽  
Fuzzy Ideal ◽  
Scientific Phenomenon ◽  
Fuzzy Topological Spaces

The fusion of technology and science is a very complex and scientific phenomenon that still carries mysteries that need to be understood. To unravel these phenomena, mathematical models are beneficial to treat different systems with unpredictable system elements. Here, the generalized intuitionistic fuzzy ideal is studied with topological space. These concepts are useful to analyze new generalized intuitionistic models. The basic structure is studied here with various relations between the generalized intuitionistic fuzzy ideals and the generalized intuitionistic fuzzy topologies. This study includes intuitionistic fuzzy topological spaces (IFS); the fundamental definitions of intuitionistic fuzzy Hausdorff space; intuitionistic fuzzy regular space; intuitionistic fuzzy normal space; intuitionistic fuzzy continuity; operations on IFS, the compactness and separation axioms.

scholarly journals Onθ-regular spaces

1994 ◽  
Vol 17 (4) ◽  
pp. 687-692 ◽  
Author(s):  
Martin M. Kovár
Keyword(s):  
Regular Space ◽  
Topological Properties ◽  
Locally Compact ◽  
Basic Properties ◽  
Paracompact Space ◽  
Paracompact Spaces

In this paper we studyθ-regularity and its relations to other topological properties. We show that the concepts ofθ-regularity (Janković, 1985) and point paracompactness (Boyte, 1973) coincide. Regular, strongly locally compact or paracompact spaces areθ-regular. We discuss the problem when a (countably)θ-regular space is regular, strongly locally compact, compact, or paracompact. We also study some basic properties of subspaces of aθ-regular space. Some applications: A space is paracompact iff the space is countablyθ-regular and semiparacompact. A generalizedFσ-subspace of a paracompact space is paracompact iff the subspace is countablyθ-regular.

Intuitionistic Fuzzy 2-Metric Space and Some Topological Properties

2013 ◽  
pp. 245-260
Author(s):  
Q.M. Danish Lohani
Keyword(s):  
Metric Space ◽  
Normed Space ◽  
Fuzzy Metric Space ◽  
Topological Properties ◽  
Fuzzy Normed Space ◽  
Fuzzy Metric ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Normed Space ◽  
Norm Space

The notion of intuitionistic fuzzy metric space was introduced by Park (2004) and the concept of intuitionistic fuzzy normed space by Saadati and Park (2006). Recently Mursaleen and Lohani introduced the concept of intuitionistic fuzzy 2-metric space (2009) and intuitionistic fuzzy 2-norm space. This paper studies precompactness and metrizability in this new setup of intuitionistic fuzzy 2-metric space.

The topological properties of intuitionistic fuzzy rough sets

2020 ◽  
Vol 38 (1) ◽  
pp. 795-807
Author(s):  
Zia Bashir ◽  
M.G. Abbas Malik ◽  
Saba Asif ◽  
Tabasam Rashid
Keyword(s):  
Rough Sets ◽  
Topological Properties ◽  
Fuzzy Rough Sets ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Rough Sets

scholarly journals On statistical convergent sequence spaces of intuitionistic Fuzzy numbers

2018 ◽  
Vol 36 (1) ◽  
pp. 235 ◽  
Author(s):  
Shyamal Debnath ◽  
Vishnu Narayan Mishra ◽  
Jayanta Debnath
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Intuitionistic Fuzzy Number ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Inclusion Relations ◽  
Bounded Sequences

In the present paper we introduce the classes of sequence stcIFN, stc0IFN and st∞IFN of statistically convergent, statistically null and statistically bounded sequences of intuitionistic fuzzy number based on the newly defined metric on the space of all intuitionistic fuzzy numbers (IFNs). We study some algebraic and topological properties of these spaces and prove some inclusion relations too.

scholarly journals LINEARLY ORDERED SPACE WHOSE SQUARE AND HIGHER POWERS CANNOT BE CONDENSED ONTO A NORMAL SPACE

2017 ◽  
Vol 20 (10) ◽  
pp. 68-73
Author(s):  
O.I. Pavlov
Keyword(s):  
Topological Space ◽  
Normal Space ◽  
Topological Properties ◽  
Pseudocompact Spaces ◽  
Countably Compact ◽  
Ordered Space ◽  
One To One ◽  
Hereditary Properties

One of the central tasks in the theory of condensations is to describe topological properties that can be improved by condensation (i.e. a continuous one-to-one mapping). Most of the known counterexamples in the field deal with non-hereditary properties. We construct a countably compact linearly ordered (hence, monotonically normal, thus ” very strongly” hereditarily normal) topological space whose square and higher powers cannot be condensed onto a normal space. The constructed space is necessarily pseudocompact in all the powers, which complements a known result on condensations of non-pseudocompact spaces.

scholarly journals Some Topological Properties ofCbX

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Juan Carlos Ferrando
Keyword(s):  
General Condition ◽  
Regular Space ◽  
Topological Properties ◽  
Compact Sets ◽  
Completely Regular

IfXis a completely regular space, first we characterize those spacesCbXwhose compact sets are metrizable. Then we use this result to provide a general condition forXto ensure the metrizability of compact sets inCbX. Finally, we characterize those spacesCbXthat have aG-basis.

Spaces of Quasi-Measures

1999 ◽  
Vol 42 (3) ◽  
pp. 291-297 ◽  
Author(s):  
D. J. Grubb ◽  
Tim LaBerge
Keyword(s):  
Direct Proof ◽  
Normal Space ◽  
Regular Space ◽  
Completely Regular

AbstractWe give a direct proof that the space of Baire quasi-measures on a completely regular space (or the space of Borel quasi-measures on a normal space) is compact Hausdorff. We show that it is possible for the space of Borel quasi-measures on a non-normal space to be non-compact. This result also provides an example of a Baire quasi-measure that has no extension to a Borel quasi-measure. Finally, we give a concise proof of theWheeler-Shakmatov theorem, which states that if X is normal and dim(X) ≤ 1, then every quasi-measure on X extends to a measure.

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