scholarly journals Some new results on six types mappings between L-convex spaces

Filomat ◽  
2020 ◽  
Vol 34 (14) ◽  
pp. 4767-4781
Author(s):  
Xiao-Wu Zhou ◽  
Fu-Gui Shi
Keyword(s):  
Quotient Spaces ◽  
Quotient Mappings ◽  
Convex Spaces

The aim of this paper is devoted to present some new results on six types of special mappings between L-convex spaces. For this purpose, we first make a summary about some novel elementary properties of L-CP mappings and L-CC mappings. Secondly, we propose the definitions of almost LCC mappings, L-isomorphic mappings and L-embedding mappings and investigate their fundamental characterizations. Finally, we establish the connections between L-quotient mappings and L-quotient spaces. As a summary, we give a diagram to show the relationships among all the above-mentioned mappings.

scholarly journals Semi-quotient mappings and spaces

2016 ◽  
Vol 14 (1) ◽  
pp. 1014-1022 ◽  
Author(s):  
Moiz ud Din Khan ◽  
Rafaqat Noreen ◽  
Muhammad Siddique Bosan
Keyword(s):  
Quotient Space ◽  
Topological Groups ◽  
Quotient Spaces ◽  
Continuous Mappings ◽  
Quotient Mappings

AbstractIn this paper, we continue the study of s-topological and irresolute-topological groups. We define semi-quotient mappings which are stronger than semi-continuous mappings, and then consider semi-quotient spaces and groups. It is proved that for some classes of irresolute-topological groups (G, *, τ) the semi-quotient space G/H is regular. Semi-isomorphisms of s-topological groups are also discussed.

The arity of convex spaces

2021 ◽  
pp. 1-8
Author(s):  
Wei Yao ◽  
Ye Chen
Keyword(s):  
Convex Space ◽  
Product Spaces ◽  
Quotient Spaces ◽  
Whole Space ◽  
Strict Definition ◽  
Convex Spaces

The arity of convex spaces is a numerical feature which shows the ability of finite subsets spanning to the whole space via the hull operators. This paper gives it a formal and strict definition by introducing the truncation of convex spaces. The relations that between the arity of quotient spaces and the original spaces, that between the arity of subspaces and superspaces, that between the arity of product spaces and factors spaces, and that between the arity of disjoint sums and term spaces, are systematically studied. A mistake of a formula in [M. Van De Vel, Theory of Convex Structures, North-Holland, Amsterdam, 1993] is corrected. It is shown that a convex space is Alexandrov iff its arity is 1. The convex structures with arity ≤n are equivalent to structured sets with n-restricted hull operators.

scholarly journals Использование гомологических методов на базе итерированных спектров в функциональном анализе

2012 ◽  
Author(s):  
E.I. Smirnov
Keyword(s):  
Locally Convex Spaces ◽  
Closed Graph ◽  
Closed Graph Theorem ◽  
Inductive Limits ◽  
Quotient Spaces ◽  
New Concepts ◽  
Inductive And Projective Limits ◽  
Projective Limits ◽  
Locally Convex ◽  
Convex Spaces

We introduce new concepts of functional analysis: Hausdorff spectrum and Hausdorff limit or H-limit of Hausdorff spectrum of locally convex spaces. Particular cases of regular H-limit are projective and inductive limits of separated locally convex spaces. The class of H-spaces contains Frechet spaces and is stable under forming countable inductive and projective limits, closed subspaces and quotient spaces. Moreover, for H-space an unproved variant of the closed graph theorem holds true. Homological methods are used for proving of theorems of vanishing at zero for first derivative of Hausdorff limit functor: Haus1(X)=0.

(L, M)- fuzzy (restricted) convex derived hull spaces

2021 ◽  
pp. 1-13
Author(s):  
Xiu-Yun Wu ◽  
Chun-Yan Liao ◽  
Yan-Hui Zhao
Keyword(s):  
Convex Hull ◽  
Convex Spaces

In this paper, the notion of (L, M)- fuzzy convex derived hull spaces is introduced. It is proved that the category of (L, M)- fuzzy convex derived hull spaces is isomorphic to the category of (L, M)- fuzzy convex spaces and the category of (L, M)- fuzzy convex enclosed relation spaces. Based on this, the notion of (L, M)- fuzzy restricted convex derived hull spaces is introduced. It is further proved that the category of (L, M)- fuzzy restricted convex derived hull spaces is isomorphic to the category of (L, M)- fuzzy restricted convex hull spaces.

scholarly journals M-Hazy Vector Spaces over M-Hazy Field

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1118
Author(s):  
Faisal Mehmood ◽  
Fu-Gui Shi
Keyword(s):  
Vector Space ◽  
Linear Transformation ◽  
Binary Operation ◽  
Vector Spaces ◽  
Fundamental Properties ◽  
Classical Algebra ◽  
Important Development ◽  
Fuzzy Algebra ◽  
Convex Spaces

The generalization of binary operation in the classical algebra to fuzzy binary operation is an important development in the field of fuzzy algebra. The paper proposes a new generalization of vector spaces over field, which is called M-hazy vector spaces over M-hazy field. Some fundamental properties of M-hazy field, M-hazy vector spaces, and M-hazy subspaces are studied, and some important results are also proved. Furthermore, the linear transformation of M-hazy vector spaces is studied and their important results are also proved. Finally, it is shown that M-fuzzifying convex spaces are induced by an M-hazy subspace of M-hazy vector space.

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