scholarly journals Proper shape invariants: Tameness and movability

1996 ◽  
Vol 19 (2) ◽  
pp. 291-298
Author(s):  
Zvonko Čerin
Keyword(s):  
Topological Spaces ◽  
Shape Theory ◽  
Geometric Properties ◽  
Basic Properties ◽  
Proper Maps ◽  
Dual Forms

We study geometric properties of topological spaces called properNCℬ-tameness, properPCℬ-tameness, and properNℬ-movability, whereℬandCdenote classes of spaces. They are related to properMCℬ-tameness and properMℬ-movability from [5] and could be regarded as their dual forms. All three are invariants of a recently invented author's proper shape theory and are described by the use of proper multi-valued functions. We explore their basic properties and prove several results on their preservation under proper maps.

ON A NEW CLASS OF SEMI GENERALIZED CLOSED SETS IN STRONG GENERALIZED TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (11) ◽  
pp. 9353-9360
Author(s):  
G. Selvi ◽  
I. Rajasekaran
Keyword(s):  
Topological Spaces ◽  
Closed Set ◽  
Basic Properties ◽  
Closed Sets ◽  
New Class ◽  
Open Set ◽  
Continuous Maps

This paper deals with the concepts of semi generalized closed sets in strong generalized topological spaces such as $sg^{\star \star}_\mu$-closed set, $sg^{\star \star}_\mu$-open set, $g^{\star \star}_\mu$-closed set, $g^{\star \star}_\mu$-open set and studied some of its basic properties included with $sg^{\star \star}_\mu$-continuous maps, $sg^{\star \star}_\mu$-irresolute maps and $T_\frac{1}{2}$-space in strong generalized topological spaces.

Generalized μ(m,n)b-open and closed functions in bigeneralized topological spaces

2016 ◽  
Vol 09 (04) ◽  
pp. 1650076
Author(s):  
Methos Kristy Villar Donesa ◽  
Helen Moso Rara
Keyword(s):  
Topological Spaces ◽  
Basic Properties ◽  
Open Formula

The purpose of this paper is to introduce the notions of [Formula: see text]-open, [Formula: see text]-closed, quasi [Formula: see text]-open, and quasi [Formula: see text]-closed functions in bigeneralized topological spaces. Basic properties, characterizations and relationships between these functions are obtained.

scholarly journals On t-Neighbourhoods in Trigonometric Topological Spaces

2021 ◽  
Vol 12 (1S) ◽  
pp. 655-658
Author(s):  
S. Malathi, Et. al.
Keyword(s):  
Necessary Condition ◽  
Topological Spaces ◽  
Basic Properties ◽  
New Type ◽  
The Relationship

In this paper we introduce a new type of neighbourhoods, namely, t-neighbourhoods in trigonometric topological spaces and study their basic properties. Also, we discuss the relationship between neighbourhoods and t-neighbourhoods. Further, we give the necessary condition for t-neighbourhoods in trigonometric topological spaces.  .

A View on Fuzzy Minimal Open Sets and Fuzzy Maximal Open Sets

2015 ◽  
Vol 7 (1) ◽  
pp. 62-73 ◽  
Author(s):  
Hamid Reza Moradi
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Basic Properties ◽  
New Class ◽  
Properties And Characterization ◽  
Open Set ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces ◽  
Characterization Theorems

A nonzero fuzzy open set () of a fuzzy topological space is said to be fuzzy minimal open (resp. fuzzy maximal open) set if any fuzzy open set which is contained (resp. contains) in is either or itself (resp. either or itself). In this note, a new class of sets called fuzzy minimal open sets and fuzzy maximal open sets in fuzzy topological spaces are introduced and studied which are subclasses of open sets. Some basic properties and characterization theorems are also to be investigated.

Neutrosophic Nano Ideal Topological Structures

2018 ◽  
Author(s):  
Parimala Mani ◽  
Karthika M ◽  
jafari S ◽  
Smarandache F ◽  
Ramalingam Udhayakumar
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Topological Structures ◽  
Basic Properties ◽  
Closed Sets ◽  
Structural Space ◽  
New Type

Neutrosophic nano topology and Nano ideal topological spaces induced the authors to propose this new concept. The aim of this paper is to introduce a new type of structural space called neutrosophic nano ideal topological spaces and investigate the relation between neutrosophic nano topological space and neutrosophic nano ideal topological spaces. We define some closed sets in these spaces to establish their relationships. Basic properties and characterizations related to these sets are given.

scholarly journals On Maximal and Minimal Fuzzy Sets in I-Topological Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-11
Author(s):  
Samer Al Ghour
Keyword(s):  
Fuzzy Sets ◽  
Topological Spaces ◽  
Basic Properties

The notion of maximal fuzzy open sets is introduced. Some basic properties and relationships regarding this notion and other notions of I-topology are given. Moreover, some deep results concerning the known minimal fuzzy open sets concept are given.

scholarly journals On Topological Structures of Fuzzy Parametrized Soft Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Serkan Atmaca ◽  
İdris Zorlutuna
Keyword(s):  
Topological Structure ◽  
Topological Spaces ◽  
Soft Sets ◽  
Topological Structures ◽  
Basic Properties

We introduce the topological structure of fuzzy parametrized soft sets and fuzzy parametrized soft mappings. We define the notion of quasi-coincidence for fuzzy parametrized soft sets and investigated its basic properties. We study the closure, interior, base, continuity, and compactness and properties of these concepts in fuzzy parametrized soft topological spaces.

scholarly journals Basic Properties of Metrizable Topological Spaces

2009 ◽  
Vol 17 (3) ◽  
pp. 201-205 ◽  
Author(s):  
Karol Pąk
Keyword(s):  
Topological Space ◽  
General Topology ◽  
Topological Spaces ◽  
Basic Properties ◽  
Special Case

Basic Properties of Metrizable Topological Spaces We continue Mizar formalization of general topology according to the book [11] by Engelking. In the article, we present the final theorem of Section 4.1. Namely, the paper includes the formalization of theorems on the correspondence between the cardinalities of the basis and of some open subcover, and a discreet (closed) subspaces, and the weight of that metrizable topological space. We also define Lindelöf spaces and state the above theorem in this special case. We also introduce the concept of separation among two subsets (see [12]).

scholarly journals Small and large inductive dimension for ideal topological spaces

2021 ◽  
Vol 22 (2) ◽  
pp. 417
Author(s):  
Fotini Sereti
Keyword(s):  
Topological Spaces ◽  
Covering Dimension ◽  
Basic Properties ◽  
Inductive Dimension ◽  
Initial Stage ◽  
Small Inductive Dimension ◽  
Important Field

<p>Undoubtedly, the small inductive dimension, ind, and the large inductive dimension, Ind, for topological spaces have been studied extensively, developing an important field in Topology. Many of their properties have been studied in details (see for example [1,4,5,9,10,18]). However, researches for dimensions in the field of ideal topological spaces are in an initial stage. The covering dimension, dim, is an exception of this fact, since it is a meaning of dimension, which has been studied for such spaces in [17]. In this paper, based on the notions of the small and large inductive dimension, new types of dimensions for ideal topological spaces are studied. They are called *-small and *-large inductive dimension, ideal small and ideal large inductive dimension. Basic properties of these dimensions are studied and relations between these dimensions are investigated.</p>

scholarly journals On Sαrw-Homeomorphism in Topological Spaces

2018 ◽  
Vol 7 (4.10) ◽  
pp. 880
Author(s):  
Basavaraj M. Ittanagi ◽  
Mohan V
Keyword(s):  
Topological Spaces ◽  
Basic Properties ◽  
New Class

New class of homeomorphisms named as sαrw-homeomorphism and sαrw*-homeomorphism are explored & elaborated. Few basic properties are inspected. Their relations with some existing homeomorphisms in topological spaces are studied.  

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