scholarly journals Gradation of Continuity for Fuzzy Soft Mappings

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Vildan Çetkin
Keyword(s):  
Topological Spaces ◽  
De Morgan Algebra ◽  
Soft Mapping ◽  
Natural Way

This paper is devoted to describe the notion of a parameterized degree of continuity for mappings between L -fuzzy soft topological spaces, where L is a complete De Morgan algebra. The degrees of openness, closedness, and being a homeomorphism for the fuzzy soft mappings are also presented. The properties and characterizations of the proposed notions are pictured. Besides, the degree of continuity for a fuzzy soft mapping is unified with the degree of compactness and connectedness in a natural way.

Soft mappings on soft generalized topological spaces

2018 ◽  
Vol 27 (2) ◽  
pp. 177-190
Author(s):  
Taha Yasin Ozturk ◽  
Keyword(s):  
Topological Spaces ◽  
Soft Mapping

In the present paper, we introduce g−open soft mapping, g−closed soft mapping, g−pseudo-open soft mapping, g−quotient soft mapping on soft generalized topological spaces. Furthermore, we discuss some characterizations and some applications of them.

scholarly journals Topological characterizations of amenability and congeniality of bases

2020 ◽  
Vol 21 (1) ◽  
pp. 1
Author(s):  
Sergio R. López-Permouth ◽  
Benjamin Stanley
Keyword(s):  
Direct Product ◽  
Topological Spaces ◽  
Countable Dimension ◽  
One To One ◽  
Natural Way

<div>We provide topological interpretations of the recently introduced notions of amenability and congeniality of bases of innite dimensional algebras. In order not to restrict our attention only to the countable dimension case, the uniformity of the topologies involved is analyzed and therefore the pertinent ideas about uniform topological spaces are surveyed.</div><div><p>A basis B over an innite dimensional F-algebra A is called amenable if F<sup>B</sup>, the direct product indexed by B of copies of the eld F, can be made into an A-module in a natural way. (Mutual) congeniality is a relation that serves to identify cases when different amenable bases yield isomorphic A-modules.</p><p>(Not necessarily mutual) congeniality between amenable bases yields an epimorphism of the modules they induce. We prove that this epimorphism is one-to-one only if the congeniality is mutual, thus establishing a precise distinction between the two notions.</p></div>

Neighborhoods and convergence with respect to a closure operator

2011 ◽  
Vol 61 (5) ◽  
Author(s):  
Josef Šlapal
Keyword(s):  
Closure Operator ◽  
Topological Spaces ◽  
Filter Convergence ◽  
Categorical Closure Operator ◽  
Natural Way

AbstractWe study neighborhoods with respect to a categorical closure operator. In particular, we discuss separation and compactness obtained from neighborhoods in a natural way and compare them with the usual closure separation and closure compactness. We also introduce a concept of convergence based on using centered systems of subobjects, which naturally generalizes the classical filter convergence in topological spaces. We investigate behavior of the convergence introduced and show, among others, that it relates to the separation and compactness in natural ways.

scholarly journals Derived length for arbitrary topological spaces

1992 ◽  
Vol 15 (2) ◽  
pp. 273-277 ◽  
Author(s):  
A. J. Jayanthan
Keyword(s):  
Topological Spaces ◽  
Derived Length ◽  
Ordinal Numbers ◽  
Scattered Spaces ◽  
Natural Way

The notion of derived length is as old as that of ordinal numbers itself. It is also known as the Cantor-Bendixon length. It is defined only for dispersed (that is scattered) spaces. In this paper this notion has been extended in a natural way for all topological spaces such that all its pleasing properties are retained. In this process we solve a problem posed by V. Kannan. ([1] Page 158).

Strong N β-Compactness in L-Topological Spaces

2013 ◽  
Vol 846-847 ◽  
pp. 1278-1281
Author(s):  
Fang Juan Zhang ◽  
Shi Zhong Bai
Keyword(s):  
Topological Spaces ◽  
Arbitrary Subset ◽  
De Morgan Algebra ◽  
Strong Compactness

In this paper,the new compactness which is strong-compactness is introduced for an arbitrary-subset and for a complete distributive De Morgan algebra. The strong-compactness implies strong-III-compactness,hence it also implies strong-II-compactness,strong-I-compactness,-compactness,-compactness and Lowen's fuzzy compactness. But it is different from-compactness.When ,strong-compactness is equivalent to-compactness.

scholarly journals A Topological Approach to Chemical Organizations

2009 ◽  
Vol 15 (1) ◽  
pp. 71-88 ◽  
Author(s):  
Gil Benkö ◽  
Florian Centler ◽  
Peter Dittrich ◽  
Christoph Flamm ◽  
Bärbel M. R. Stadler ◽  
...  
Keyword(s):  
Chemical Species ◽  
Alternative Interpretation ◽  
Point Of View ◽  
Topological Spaces ◽  
Production Rules ◽  
Topological Approach ◽  
Distinctive Features ◽  
The Individual ◽  
Directed Hypergraph ◽  
Natural Way

Large chemical reaction networks often exhibit distinctive features that can be interpreted as higher-level structures. Prime examples are metabolic pathways in a biochemical context. We review mathematical approaches that exploit the stoichiometric structure, which can be seen as a particular directed hypergraph, to derive an algebraic picture of chemical organizations. We then give an alternative interpretation in terms of set-valued set functions that encapsulate the production rules of the individual reactions. From the mathematical point of view, these functions define generalized topological spaces on the set of chemical species. We show that organization-theoretic concepts also appear in a natural way in the topological language. This abstract representation in turn suggests the exploration of the chemical meaning of well-established topological concepts. As an example, we consider connectedness in some detail.

I-Subsemigroups and α-monomorphisms

1973 ◽  
Vol 16 (2) ◽  
pp. 146-166 ◽  
Author(s):  
Kenneth D. Magill
Keyword(s):  
Topological Space ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Natural Way

To each idempotent v of a semigroup T, there is associated, in a natural way, a subsemigroup Tv of T. The subsemigroup Tv is simply the collection of all elements of T for which v acts as a two-sided identity. We refer to such a subsemigroup as an I-subsemigroup of T. We first establish some elementary properties of these subsemigroups with no restrictions on the semigroup in which they are contained. Then we turn our attention to the semigroup of all continuous selfmaps of a topological space. The I-subsemigroups of these semigroups are investigated in some detail and so are the a-monomorphisms [3, p. 518] from one such semigroup into another. Among other things, a relationship is established between I-subsemigroups and α-monomorphisms. An analogous theory exists for semigroups of closed selfmaps on topological spaces. A number of results are listed for these semigroups with the proofs often deleted since, in many cases, the situation is much the same as for semigroups of continuous functions.

γ-Operation and Some Types of Soft Sets and Soft Continuity of (Supra) Soft Topological Spaces

2016 ◽  
pp. 127-171
Author(s):  
Ali Kandil ◽  
Osama A. El-Tantawy ◽  
Sobhy A. El-Sheikh ◽  
A. M. Abd El-latif
Keyword(s):  
Topological Space ◽  
Soft Set ◽  
Topological Spaces ◽  
Topological Properties ◽  
Soft Sets ◽  
Soft Mapping ◽  
Separation Axioms ◽  
Different Types

The main purpose of this chapter is to introduce the notions of ?-operation, pre-open soft set a-open sets, semi open soft set and ß-open soft sets to soft topological spaces. We study the relations between these different types of subsets of soft topological spaces. We introduce new soft separation axioms based on the semi open soft sets which are more general than of the open soft sets. We show that the properties of soft semi Ti-spaces (i=1,2) are soft topological properties under the bijection and irresolute open soft mapping. Also, we introduce the notion of supra soft topological spaces. Moreover, we introduce the concept of supra generalized closed soft sets (supra g-closed soft for short) in a supra topological space (X,µ,E) and study their properties in detail.

Developability and Some New Regularity Axioms

1981 ◽  
Vol 33 (3) ◽  
pp. 641-663 ◽  
Author(s):  
N. C. Heldermann
Keyword(s):  
Continuous Function ◽  
Closed Subset ◽  
Natural Extension ◽  
Unit Interval ◽  
Regularity Conditions ◽  
Regular Space ◽  
Topological Spaces ◽  
Completely Regular ◽  
Natural Way

In a recent publication H. Brandenburg [5] introduced D-completely regular topological spaces as a natural extension of completely regular (not necessarily T1) spaces: Whereas every closed subset A of a completely regular space X and every x ∈ X\A can be separated by a continuous function into a pseudometrizable space (namely into the unit interval), D-completely regular spaces admit such a separation into developable spaces. In analogy to the work of O. Frink [16], J. M. Aarts and J. de Groot [19] and others ([38], [46]), Brandenburg derived a base characterization of D-completely regular spaces, which gives rise in a natural way to two new regularity conditions, D-regularity and weak regularity.

VARIETIES OF EQUALITY STRUCTURES

2003 ◽  
Vol 13 (04) ◽  
pp. 463-480 ◽  
Author(s):  
DESMOND FEARNLEY-SANDER ◽  
TIM STOKES
Keyword(s):  
Binary Operation ◽  
Topological Spaces ◽  
Natural Conditions ◽  
Universal Algebras ◽  
Natural Way

We consider universal algebras which are monoids and which have a binary operation we call internalized equality, satisfying some natural conditions. We show that the class of such E-structures has a characterization in terms of a distinguished submonoid which is a semilattice. Some important varieties (and variety-like classes) of E-structures are considered, including E-semilattices (which we represent in terms of topological spaces), E-rings (which we show are equivalent to rings with a generalized interior operation), E-quantales (where internalized equalities on a fixed quantale in which 1 is the largest element are shown to correspond to sublocales of the quantale), and EI-structures (in which an internalized inequality is defined and interacts in a natural way with the equality operation).

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