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>

Connectedness Between Soft Sets

2018 ◽  
Vol 14 (01) ◽  
pp. 53-71 ◽  
Author(s):  
Samajh Singh Thakur ◽  
Alpa Singh Rajput
Keyword(s):  
Soft Set ◽  
Topological Spaces ◽  
Soft Sets ◽  
Continuous Mappings ◽  
Weakly Continuous

In the present paper, the concepts of soft connectedness between soft sets, soft set-connected and soft weakly continuous mappings in soft topological spaces have been introduced and studied.

Nearnesses and T0-Extensions of Topological Spaces

1983 ◽  
Vol 26 (4) ◽  
pp. 430-437 ◽  
Author(s):  
Alice M. Dean
Keyword(s):  
Topological Space ◽  
Equivalence Classes ◽  
Topological Spaces ◽  
One To One

AbstractIn [3], Reed establishes a bijection between the (equivalence classes of) principal T1-extensions of a topological space X and the compatible, cluster-generated, Lodato nearnesses on X. We extend Reed's result to the T0 case by obtaining a one-to-one correspondence between the principal T0-extensions of a space X and the collections of sets (called “t-grill sets”) which generate a certain class of nearnesses which we call “t-bunch generated” nearnesses. This correspondence specializes to principal T0-compactifications. Finally, we show that there is a bijection between these t-grill sets and the filter systems of Thron [5], and that the corresponding extensions are equivalent.

Soft almost \(\alpha\)-continuous mappings

2018 ◽  
Vol 9 (2) ◽  
pp. 94-99 ◽  
Author(s):  
S. S. Thakur ◽  
A. S. Rajput
Keyword(s):  
Topological Spaces ◽  
Continuous Mappings

In the present paper the concept of soft almost \(\alpha\)-continuous mappings and soft almost \(\alpha\)-open mappings in soft topological spaces have been introduced and studied.

scholarly journals On induced map f# in fuzzy set theory and its applications to fuzzy continuity

2021 ◽  
Author(s):  
Sandeep Kaur ◽  
Nitakshi Goyal
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Closure Operator ◽  
Topological Spaces ◽  
Continuous Mappings ◽  
New Vision ◽  
Saturated Sets ◽  
Interior Operator ◽  
Fuzzy Topological Spaces

Abstract In this paper, we introduce # image of a fuzzy set which gives a induced map f # corresponding to any function f : X → Y , where X and Y are crisp sets. With this, we present a new vision of studying fuzzy continuous mappings in fuzzy topological spaces where fuzzy continuity explains the term of closeness in the mathematical models. We also define the concept of fuzzy saturated sets which helps us to prove some new characterizations of fuzzy continuous mappings in terms of interior operator rather than closure operator.

scholarly journals A New Type of Strongly Faint Continuous Mappings and Their Applications in Topological Spaces

2019 ◽  
Vol 14 (3) ◽  
pp. 905-912 ◽  
Author(s):  
Alaa M.F. Al. Jumaili ◽  
Alaa A. Auad ◽  
Majid Mohammed Abed
Keyword(s):  
Topological Spaces ◽  
Continuous Mappings ◽  
New Type
Sign in / Sign up

Export Citation Format

Share Document