scholarly journals Function spaces based on L-sets

Filomat ◽  
2020 ◽  
Vol 34 (11) ◽  
pp. 3815-3834
Author(s):  
Jinming Fang ◽  
Yueli Yue
Keyword(s):  
Function Spaces ◽  
Concrete Category ◽  
Convergence Spaces ◽  
Cartesian Closed

For a commutative, integral, and divisible quantale L, a concept of top L-convergence spaces based on L-sets other than crisp sets is proposed by using a kind of L-filters, namely limited L-filters defined in the paper. Our main result is the existence of function spaces in the the concrete category of top L-convergence spaces over the slice category Set#L rather than the category Set of sets, such that the concrete category of top L-convergence spaces over the slice category Set#L is Cartesian closed. In order to support the existence of top L-convergence spaces, some nontrivial examples of limited L-filters and top L-convergence spaces are presented also.

scholarly journals The category of uniform convergence spaces is cartesian closed

1976 ◽  
Vol 15 (3) ◽  
pp. 461-465 ◽  
Author(s):  
R.S. Lee
Keyword(s):  
Uniform Convergence ◽  
Function Spaces ◽  
Convergence Spaces ◽  
Cartesian Closedness ◽  
Cartesian Closed ◽  
And Function

This paper first assigns specific uniform convergence structures to the products and function spaces of pairs of uniform convergence spaces, and then establishes a bijection between corresponding sets of morphisms which yields cartesian closedness.

scholarly journals A Study on Cubic H-Relations in a Topological Universe Viewpoint

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 482
Author(s):  
Jeong-Gon Lee ◽  
Kul Hur ◽  
Xueyou Chen
Keyword(s):  
Concrete Category ◽  
Cartesian Closed

We introduce the concrete category CRel P ( H ) [resp. CRel R ( H ) ] of cubic H-relational spaces and P-preserving [resp. R-preserving] mappings between them and study it in a topological universe viewpoint. In addition, we prove that it is Cartesian closed over Set . Next, we introduce the subcategory CRel P , R ( H ) [resp. CRel R , R ( H ) ] of CRel P ( H ) [resp. CRel R ( H ) ] and investigate it in the sense of a topological universe. In particular, we obtain exponential objects in CRel P , R ( H ) [resp. CRel R , R ( H ) ] quite different from those in CRel P ( H ) [resp. CRel R ( H ) ].

scholarly journals On fuzzy function spaces

1999 ◽  
Vol 22 (4) ◽  
pp. 727-737 ◽  
Author(s):  
Gunther Jäger
Keyword(s):  
Function Spaces ◽  
Compact Open Topology ◽  
Convergence Spaces ◽  
Exponential Law ◽  
Fuzzy Function ◽  
Fuzzy Convergence ◽  
Special Case ◽  
Fuzzy Subsets

In [3], we started the investigation of compactness in fuzzy function spaces in FCS, the category of fuzzy convergence spaces as defined by Lowen/Lowen/Wuyts [8]. This paper goes somewhat deeper in the investigation of fuzzy function spaces using the notion of splitting and conjoining structures on fuzzy subsets. We discuss the connection to the exponential law and give several examples of such structures. As a special case, we study a notion of fuzzy compact open topology.

scholarly journals On the continuous action of enriched lattice-valued convergence groups: Some examples

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 3045-3064
Author(s):  
T.M.G. Ahsanullah ◽  
Fawzi Al-Thukair ◽  
Jawaher Al-Mufarrij
Keyword(s):  
Transformation Group ◽  
Transformation Groups ◽  
Triangular Norm ◽  
Topological Transformation ◽  
Continuous Action ◽  
Convergence Spaces ◽  
Group A ◽  
Convergence Approach Spaces ◽  
Cartesian Closed ◽  
Approach Spaces

Starting with a category SL-CONVGRP, of stratified enriched cl-premonoid-valued convergence groups as introduced earlier, we present a category SL-CONVTGRP, of stratified enriched cl-premonoid-valued convergence transformation groups, the idea behind this category is crept in the notion of convergence transformation group - a generalization of topological transformation group. In this respect, we are able to provide natural examples in support to our endeavor; these examples, however, stem from the action of convergence approach groups on convergence approach spaces, and the action of probabilistic convergence groups under triangular norm on probabilistic convergence spaces. Based on the category of enriched lattice-valued convergence spaces, a Cartesian closed category that enjoys lattice-valued convergence structure on function space, we look into among others, the lattice-valued convergence structures on the group of homeomorphisms of enriched lattice-valued convergence spaces, generalizing a concept of convergence transformation groups on convergence spaces, obtaining a characterization.

Function Spaces and Nonsymmetric Norm Preserving Maps

2018 ◽  
Vol 25 (5) ◽  
pp. 729-740
Author(s):  
Hadis Pazandeh ◽  
Fereshteh Sady
Keyword(s):  
Function Spaces

The Mehler-Fock-Clifford transform and pseudo-differential operator on function spaces

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2457-2469
Author(s):  
Akhilesh Prasad ◽  
S.K. Verma
Keyword(s):  
Differential Operator ◽  
Function Spaces ◽  
Pseudo Differential Operator ◽  
Test Function ◽  
Basic Properties ◽  
Cone Function ◽  
Translation Operators

In this article, weintroduce a new index transform associated with the cone function Pi ??-1/2 (2?x), named as Mehler-Fock-Clifford transform and study its some basic properties. Convolution and translation operators are defined and obtained their estimates under Lp(I, x-1/2 dx) norm. The test function spaces G? and F? are introduced and discussed the continuity of the differential operator and MFC-transform on these spaces. Moreover, the pseudo-differential operator (p.d.o.) involving MFC-transform is defined and studied its continuity between G? and F?.

Topologies Between Compact and Uniform Convergence on Function Spaces, II

1992 ◽  
Vol 18 (1) ◽  
pp. 176 ◽  
Author(s):  
Kundu ◽  
McCoy ◽  
Raha
Keyword(s):  
Uniform Convergence ◽  
Function Spaces
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