scholarly journals On (fuzzy) pseudo-semi-normed linear spaces

2021 ◽  
Vol 7 (1) ◽  
pp. 467-477
Author(s):  
Yaoqiang Wu ◽  
Keyword(s):  
The Other ◽  
Topological Spaces ◽  
Normed Spaces ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Other Hand ◽  
Fuzzy Topological Spaces

<abstract><p>In this paper, we introduce the notion of pseudo-semi-normed linear spaces, following the concept of pseudo-norm which was presented by Schaefer and Wolff, and illustrate their relationship. On the other hand, we introduce the concept of fuzzy pseudo-semi-norm, which is weaker than the notion of fuzzy pseudo-norm initiated by N$ \tilde{\rm{a}} $d$ \tilde{\rm{a}} $ban. Moreover, we give some examples which are according to the commonly used $ t $-norms. Finally, we establish norm structures of fuzzy pseudo-semi-normed spaces and provide (fuzzy) topological spaces induced by (fuzzy) pseudo-semi-norms, and prove that the (fuzzy) topological spaces are (fuzzy) Hausdorff.</p></abstract>

Postnikov “Invariants” in 2004

2005 ◽  
Vol 12 (1) ◽  
pp. 139-155
Author(s):  
Julio Rubio ◽  
Francis Sergeraert
Keyword(s):  
Decision Problem ◽  
The Other ◽  
Topological Spaces ◽  
Exact Nature ◽  
Other Hand

Abstract The very nature of the so-called Postnikov invariants is carefully studied. Two functors, precisely defined, explain the exact nature of the connection between the category of topological spaces and the category of Postnikov towers. On one hand, these functors are in particular effective and lead to concrete machine computations through the general machine program Kenzo. On the other hand, the Postnikov “invariants” will be actual invariants only when an arithmetical decision problem – currently open – will be solved; it is even possible this problem is undecidable.

scholarly journals Multilinear Operator and Its Basic Properties

2019 ◽  
Vol 27 (1) ◽  
pp. 35-45
Author(s):  
Kazuhisa Nakasho
Keyword(s):  
Algebraic Structure ◽  
Multilinear Operator ◽  
Multilinear Operators ◽  
Normed Spaces ◽  
Linear Spaces ◽  
Basic Properties ◽  
Normed Linear Spaces ◽  
Real Linear

Summary In the first chapter, the notion of multilinear operator on real linear spaces is discussed. The algebraic structure [2] of multilinear operators is introduced here. In the second chapter, the results of the first chapter are extended to the case of the normed spaces. This chapter shows that bounded multilinear operators on normed linear spaces constitute the algebraic structure. We referred to [3], [7], [5], [6] in this formalization.

scholarly journals Some Results on G-Normed Linear Spaces

2020 ◽  
Vol 55 (3) ◽  
Author(s):  
Maiada Nazar Mohammedali ◽  
Raghad Ibraham Sabri ◽  
Mohammed Rasheed ◽  
Suha Shihab
Keyword(s):  
Normed Space ◽  
Cartesian Product ◽  
Normed Spaces ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Definition Of

In the present work, our goal is to define the Cartesian product of two generalized normed spaces depending on the notion of generalized normed space. It is a background to state and prove that the Cartesian product of two complete generalized normed spaces is also a complete generalized normed space. Furthermore, the definition of the pseudo-generalized normed space is introduced and essential concepts related to this space are discussed and proved.

scholarly journals Weakly b-Closed Sets and Weakly b-Open Sets based of Fuzzy Neutrosophic bi-Topological Spaces

2020 ◽  
pp. 34-43
Author(s):  
Fatimah M. .. ◽  
◽  
◽  
Sarah W. Raheem
Keyword(s):  
The Other ◽  
Topological Spaces ◽  
Neutrosophic Sets ◽  
Basic Properties ◽  
Closed Sets ◽  
New Class ◽  
Other Hand ◽  
Definition Of

In this paper, we present and study some of the basic properties of the new class of sets called weakly b-closed sets and weakly b- open sets in fuzzy neutrosophic bi-topological spaces. We referred to some results related to the new definitions, which we taked the case of equal in the definition of b-sets instead of subset. Then, we discussed the relations between the new defined sets by hand and others fuzzy neutrosophic sets which were studied before us on the other hand on fuzzy neutrosophic bi-topological spaces. Then, we have studied some of characteristics and some relations are compared with necessary examples.

scholarly journals The Fuzzification of Classical Structures: A General View

2015 ◽  
Vol 10 (6) ◽  
pp. 12 ◽  
Author(s):  
Ioan Dzitac
Keyword(s):  
Metric Spaces ◽  
50Th Anniversary ◽  
Vector Spaces ◽  
Fuzzy Mathematics ◽  
Future Research ◽  
Topological Spaces ◽  
General View ◽  
Linear Spaces ◽  
Topological Vector Spaces ◽  
Fuzzy Topological Spaces

The aim of this survey article, dedicated to the 50th anniversary of Zadeh’s pioneering paper "Fuzzy Sets" (1965), is to offer a unitary view to some important spaces in fuzzy mathematics: fuzzy real line, fuzzy topological spaces, fuzzy metric spaces, fuzzy topological vector spaces, fuzzy normed linear spaces. We believe that this paper will be a support for future research in this field.

scholarly journals Tilings in topological spaces

1999 ◽  
Vol 22 (3) ◽  
pp. 611-616 ◽  
Author(s):  
F. G. Arenas
Keyword(s):  
Topological Space ◽  
Pairwise Disjoint ◽  
The Other ◽  
Vector Spaces ◽  
Topological Spaces ◽  
Topological Vector Spaces ◽  
Other Hand ◽  
Extensive Bibliography

Atilingof a topological spaceXis a covering ofXby sets (calledtiles) which are the closures of their pairwise-disjoint interiors. Tilings ofℝ2have received considerable attention (see [2] for a wealth of interesting examples and results as well as an extensive bibliography). On the other hand, the study of tilings of general topological spaces is just beginning (see [1, 3, 4, 6]). We give some generalizations for topological spaces of some results known for certain classes of tilings of topological vector spaces.

scholarly journals Spaces of vector functions that are integrable with respect to vector measures

2007 ◽  
Vol 82 (1) ◽  
pp. 85-109 ◽  
Author(s):  
José Rodríguez
Keyword(s):  
Banach Space ◽  
Probability Space ◽  
Equivalence Classes ◽  
The Other ◽  
Normed Spaces ◽  
Vector Measures ◽  
Other Hand ◽  
Integrable Functions ◽  
Compact Range ◽  
Indefinite Integral

AbstractWe study the normed spaces of (equivalence classes of) Banach space-valued functions that are Dobrakov,S* or McShane integrable with respect to a Banach space-valued measure, where the norm is the natural one given by the total semivariation of the indefinite integral. We show that simple functions are dense in these spaces. As a consequence we characterize when the corresponding indefinite integrals have norm relatively compact range. On the other hand, we also determine when these spaces are ultrabornological. Our results apply to conclude, for instance, that the spaces of Birkhoff (respectively McShane) integrable functions defined on a complete (respectively quasi-Radon) probability space, endowed with the Pettis norm, are ultrabornological.

p-semisimple modules and type submodules

2019 ◽  
Vol 19 (04) ◽  
pp. 2050078
Author(s):  
A. Mozaffarikhah ◽  
E. Momtahan ◽  
A. R. Olfati ◽  
S. Safaeeyan
Keyword(s):  
Abelian Groups ◽  
Large Family ◽  
The Other ◽  
Topological Spaces ◽  
Algebraic Structures ◽  
Semisimple Modules ◽  
Other Hand ◽  
One To One ◽  
Regular Closed

In this paper, we introduce the concept of [Formula: see text]-semisimple modules. We prove that a multiplication reduced module is [Formula: see text]-semisimple if and only if it is a Baer module. We show that a large family of abelian groups are [Formula: see text]-semisimple. Furthermore, we give a topological characterizations of type submodules (ideals) of multiplication reduced modules ([Formula: see text]-semisimple rings). Moreover, we observe that there is a one-to-one correspondence between type ideals of some algebraic structures on one hand and regular closed subsets of some related topological spaces on the other hand. This also characterizes the form of closed ideals in [Formula: see text].

scholarly journals The smallest proper congruence on S(X)

1988 ◽  
Vol 30 (3) ◽  
pp. 301-313 ◽  
Author(s):  
K. H. Hofmann ◽  
K. D. Magill
Keyword(s):  
Topological Space ◽  
Complete Lattice ◽  
The Other ◽  
Topological Spaces ◽  
Other Hand ◽  
Dual Atom ◽  
Lattice Of Congruences

S(X) is the semigroup of all continuous self maps of the topological space X and for any semigroup S, Cong(S) will denote the complete lattice of congruences on S. Cong(S) has a zero Z and a unit U. Specifically, Z = {(a, a):a ∈ S} and U = S × S. Evidently, Z and U are distinct if S has at least two elements. By a proper congruence on S we mean any congruence which differs from each of these. Since S(X) has more than one element when X is nondegenerate, we will assume without further mention that the spaces we discuss in this paper have more than one point. We observed in [4] that there are a number of topological spaces X such that S(X) has a largest proper congruence, that is, Cong(S(X)) has a unique dual atom which is greater than every other proper congruence on S(X). On the other hand, we also found out in [5] that it is also common for S(X) to fail to have a largest proper congruence. We will see that the situation is quite different at the other end of the spectrum in that it is rather rare for S(X) not to have a smallest proper congruence. In other words, for most spaces X, Cong(S(X)) has a unique atom which is smaller than every other proper congruence.

scholarly journals RegularL-fuzzy topological spaces and their topological modifications

2000 ◽  
Vol 23 (10) ◽  
pp. 687-695 ◽  
Author(s):  
T. Kubiak ◽  
M. A. de Prada Vicente
Keyword(s):  
Topological Space ◽  
The Other ◽  
Regular Space ◽  
Continuous Lattice ◽  
Topological Spaces ◽  
Scott Topology ◽  
Fuzzy Topological Spaces

ForLa continuous lattice with its Scott topology, the functorιLmakes every regularL-topological space into a regular space and so does the functorωLthe other way around. This has previously been known to hold in the restrictive class of the so-called weakly induced spaces. The concepts ofH-Lindelöfness (á la Hutton compactness) is introduced and characterized in terms of certain filters. RegularH-Lindelöf spaces are shown to be normal.

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