scholarly journals CONTINUOUS ORDER REPRESENTABILITY PROPERTIES OF TOPOLOGICAL SPACES AND ALGEBRAIC STRUCTURES

2012 ◽  
Vol 49 (3) ◽  
pp. 449-473 ◽  
Author(s):  
Maria Jesus Campion ◽  
Juan Carlos Candeal ◽  
Esteban Indurain ◽  
Ghanshyam Bhagvandas Mehta
Keyword(s):  
Topological Spaces ◽  
Algebraic Structures

scholarly journals Real algebraic structures on topological spaces

1981 ◽  
Vol 53 (1) ◽  
pp. 79-162 ◽  
Author(s):  
Selman Akbulut ◽  
Henry C. King
Keyword(s):  
Topological Spaces ◽  
Algebraic Structures

Some lattices associated with LM-fuzzy topological spaces

2021 ◽  
pp. 1-9
Author(s):  
S. Vivek ◽  
Sunil C. Mathew
Keyword(s):  
Topological Spaces ◽  
Algebraic Structures ◽  
Closed Sets ◽  
Fuzzy Topological Spaces

This paper studies the closure and interior operators in LM-fuzzy topological spaces. The algebraic structures associated with various collections of closed sets and open sets are identified. Further, certain lattices formed by these algebraic structures are obtained and some lattice theoretic properties of the same are investigated. Corresponding to every element in M, the study associates a lattice of monoids which is determined by various types of closed sets and open sets.

scholarly journals (m, n)-Ideals in Semigoups Based on Int-Soft Sets

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
G. Muhiuddin ◽  
Abdulaziz M. Alanazi
Keyword(s):  
Coding Theory ◽  
Abstract Algebra ◽  
Theoretical Physics ◽  
Topological Spaces ◽  
Algebraic Structures ◽  
Soft Sets ◽  
Control Engineering ◽  
Regular Semigroups ◽  
Engineering Information ◽  
Fuzzy Setting

Algebraic structures play a prominent role in mathematics with wide ranging applications in many disciplines such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, and topological spaces. This provides sufficient motivation to researchers to review various concepts and results from the realm of abstract algebra in the broader framework of fuzzy setting. In this paper, we introduce the notions of int-soft m , n -ideals, int-soft m , 0 -ideals, and int-soft 0 , n -ideals of semigroups by generalizing the concept of int-soft bi-ideals, int-soft right ideals, and int-soft left ideals in semigroups. In addition, some of the properties of int-soft m , n -ideal, int-soft m , 0 -ideal, and int-soft 0 , n -ideal are studied. Also, characterizations of various types of semigroups such as m , n -regular semigroups, m , 0 -regular semigroups, and 0 , n -regular semigroups in terms of their int-soft m , n -ideals, int-soft m , 0 -ideals, and int-soft 0 , n -ideals are provided.

scholarly journals Analysis of Topological Endomorphism of Fuzzy Measure in Hausdorff Distributed Monoid Spaces

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 671
Author(s):  
Susmit Bagchi
Keyword(s):  
Comparative Analysis ◽  
Topological Space ◽  
Fuzzy Sets ◽  
Fuzzy Measure ◽  
Topological Spaces ◽  
Algebraic Structures ◽  
Fuzzy Measures ◽  
And Topology ◽  
Analytical Properties ◽  
Topological Measures

The concepts of fuzzy sets and topology are widely applied to model various algebraic structures and computations. The dynamics of fuzzy measures in topological spaces having distributed monoid embeddings is an interesting topic in the presence of topological endomorphism. This paper presents the analysis of topological endomorphism and the properties of topological fuzzy measures in distributed monoid spaces. The topological space is considered to be Hausdorff and second countable in nature. The analysis of consistency of fuzzy measure in endomorphic topological spaces is formulated. The algebraic structures of endomorphic topological spaces having distributed cyclic monoids are constructed. The cyclic monoids contain specific generators, and a related cyclic topological endomorphism within the subspace is formulated. The analytical properties of fuzzy topological measures in the presence of cyclic topological endomorphism are presented. A comparative analysis of this proposed work with other related work in the domain is included.

Formalising Overlap Algebras in Matita

2011 ◽  
Vol 21 (4) ◽  
pp. 763-793 ◽  
Author(s):  
CLAUDIO SACERDOTI COEN ◽  
ENRICO TASSI
Keyword(s):  
Intuitionistic Logic ◽  
Scientific Collaboration ◽  
Optimal Solution ◽  
The Other ◽  
Theorem Prover ◽  
Topological Spaces ◽  
Algebraic Structures ◽  
Size Information ◽  
Predicative Logic

We describe some formal topological results, formalised in Matita 1/2, presented in predicative intuitionistic logic and in terms of Overlap Algebras.Overlap Algebras are new algebraic structures designed to ease reasoning about subsets in an algebraic way within intuitionistic logic. We find that they also ease the formalisation of formal topological results in an interactive theorem prover.Our main result is the existence of a functor between two categories of ‘generalised topological spaces’, one with points (Basic Pairs) and the other point-free (Basic Topologies). This formalisation is part of a wider scientific collaboration with the inventor of the theory, Giovanni Sambin. His goal is to verify in what sense his theory is ‘implementable’, and to discover what problems may arise in the process. We check that all intermediate constructions respect the stringent size requirements imposed by predicative logic. The formalisation is quite unusual, since it has to make explicit size information that is often hidden.We found that the version of Matita used for the formalisation was largely inappropriate. The formalisation drove several major improvements of Matita that will be integrated in the next major release (Matita 1.0). We show some motivating examples, taken directly from the formalisation, for these improvements. We also describe a possibly sub-optimal solution in Matita 1/2, which is exploitable in other similar systems. We briefly discuss a better solution available in Matita 1.0.

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 Algebras with actions and automata

1982 ◽  
Vol 5 (1) ◽  
pp. 61-85
Author(s):  
W. Kühnel ◽  
M. Pfender ◽  
J. Meseguer ◽  
I. Sols
Keyword(s):  
Axiomatic Approach ◽  
Structure Theory ◽  
Topological Spaces ◽  
Algebraic Structures ◽  
Hausdorff Spaces ◽  
Left Action ◽  
Common Structure ◽  
The One ◽  
Cartesian Closed ◽  
In The Beginning

In the present paper we want to give a common structure theory of left action, group operations,R-modules and automata of different types defined over various kinds of carrier objects: sets, graphs, presheaves, sheaves, topological spaces (in particular: compactly generated Hausdorff spaces). The first section gives an axiomatic approach to algebraic structures relative to a base categoryB, slightly more powerful than that of monadic (tripleable) functors. In section2we generalize Lawveres functorial semantics to many-sorted algebras over cartesian closed categories. In section3we treat the structures mentioned in the beginning as many-sorted algebras with fixed “scalar” or “input” object and show that they still have an algebraic (or monadic) forgetful functor (theorem 3.3) and hence the general theory of algebraic structures applies. These structures were usually treated as one-sorted in the Lawvere-setting, the action being expressed by a family of unary operations indexed over the scalars. But this approach cannot, as the one developed here, describe continuity of the action (more general: the action to be aB-morphism), which is essential for the structures mentioned above, e.g. modules for a sheaf of rings or topological automata. Finally we discuss consequences of theorem 3.3 for the structure theory of various types of automata. The particular case of algebras with fixed “natural numbers object” has been studied by the authors in [23].

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