Soft topological product space

2017 ◽  
Author(s):  
Li Fu ◽  
Hua Fu ◽  
Fei You
Keyword(s):  
Product Space ◽  
Topological Product

The Structure of Continuous {0, 1}-Valued Functions on a Topological Product

1976 ◽  
Vol 28 (3) ◽  
pp. 553-559 ◽  
Author(s):  
S. Broverman
Keyword(s):  
Product Space ◽  
Discrete Space ◽  
Topological Product

In this paper we investigate the question of which continuous ﹛0, 1﹜-valued functions on a product space admit continuous extensions to where βXα is the Stone-Čech compactification of Xa and ﹛0, 1﹜ denotes the two point discrete space. This problem is clearly equivalent to determining which clopen subsets of have clopen closures in .

Homology of Deleted Products of Contractible 2-Dimensional Polyhedra. I

1968 ◽  
Vol 20 ◽  
pp. 416-441
Author(s):  
C. W. Patty
Keyword(s):  
Product Space ◽  
Topological Product ◽  
Homology Groups

If X is a space and , the kth deleted product space Xk* of X is the topological product X ⨯ X ⨯ . . . ⨯ X of copies of X minus the set of all points of the form (x, x, . . . , x), where x ∊ X. In (4), the author shows that the homology groups of Xk*, where X is a tree, produce as much information about trees as counting the orders of vertices.

The Incentives to, and Constraints upon, Product Innovation

2018 ◽  
Author(s):  
Paul Stoneman ◽  
Eleonora Bartoloni ◽  
Maurizio Baussola
Keyword(s):  
Survey Data ◽  
Product Innovation ◽  
Product Space ◽  
Driving Forces ◽  
Product Line ◽  
Decision Uncertainty ◽  
Market Structures ◽  
Product Innovations

This chapter explores the factors that affect the firm’s decision to undertake product innovation. The discussion encompasses the driving forces that encourage product innovation, for example innovation by others or the ageing of an existing product line; however, the basic rationale is the search for profits. The chapter also addresses decisions about: the extent of innovation in general; horizontal and vertical product innovations separately; and the location of innovations in product space. The role of market structures in the product innovation decision, uncertainty in the innovating environment, and issues relating to emulation and copying are also addressed. Constraints to product innovation that survey data indicate are most important—innovation costs, risk and finance, and the availability of qualified labour—are also addressed.

scholarly journals Fractal Frames of Functions on the Rectangle

2021 ◽  
Vol 5 (2) ◽  
pp. 42
Author(s):  
María A. Navascués ◽  
Ram Mohapatra ◽  
Md. Nasim Akhtar
Keyword(s):  
Tensor Product ◽  
Product Space ◽  
Integrable Function ◽  
Two Dimensional ◽  
Tensor Product Space ◽  
Fractal Functions

In this paper, we define fractal bases and fractal frames of L2(I×J), where I and J are real compact intervals, in order to approximate two-dimensional square-integrable maps whose domain is a rectangle, using the identification of L2(I×J) with the tensor product space L2(I)⨂L2(J). First, we recall the procedure of constructing a fractal perturbation of a continuous or integrable function. Then, we define fractal frames and bases of L2(I×J) composed of product of such fractal functions. We also obtain weaker families as Bessel, Riesz and Schauder sequences for the same space. Additionally, we study some properties of the tensor product of the fractal operators associated with the maps corresponding to each variable.

scholarly journals On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 116
Author(s):  
Qi Liu ◽  
Yongjin Li
Keyword(s):  
Banach Spaces ◽  
Product Space ◽  
Sufficient Conditions ◽  
Normal Structure ◽  
The Other ◽  
Inner Product ◽  
Equivalent Characterization ◽  
Geometric Constant ◽  
Geometric Constants

In this paper, we will introduce a new geometric constant LYJ(λ,μ,X) based on an equivalent characterization of inner product space, which was proposed by Moslehian and Rassias. We first discuss some equivalent forms of the proposed constant. Next, a characterization of uniformly non-square is given. Moreover, some sufficient conditions which imply weak normal structure are presented. Finally, we obtain some relationship between the other well-known geometric constants and LYJ(λ,μ,X). Also, this new coefficient is computed for X being concrete space.

scholarly journals Fuzzy Inner Product Space: Literature Review and a New Approach

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 765
Author(s):  
Lorena Popa ◽  
Lavinia Sida
Keyword(s):  
Literature Review ◽  
Product Space ◽  
Inner Product Space ◽  
Inner Product ◽  
Product Spaces ◽  
Comprehensive Overview ◽  
New Approach ◽  
Inner Product Spaces ◽  
Product Function ◽  
Suitable Definition

The aim of this paper is to provide a suitable definition for the concept of fuzzy inner product space. In order to achieve this, we firstly focused on various approaches from the already-existent literature. Due to the emergence of various studies on fuzzy inner product spaces, it is necessary to make a comprehensive overview of the published papers on the aforementioned subject in order to facilitate subsequent research. Then we considered another approach to the notion of fuzzy inner product starting from P. Majundar and S.K. Samanta’s definition. In fact, we changed their definition and we proved some new properties of the fuzzy inner product function. We also proved that this fuzzy inner product generates a fuzzy norm of the type Nădăban-Dzitac. Finally, some challenges are given.

Mackey Continuity of Characteristic Functionals

2002 ◽  
Vol 9 (1) ◽  
pp. 83-112
Author(s):  
S. Kwapień ◽  
V. Tarieladze
Keyword(s):  
Product Space ◽  
Locally Convex Space ◽  
Inner Product ◽  
Nuclear Space ◽  
Probability Measures ◽  
Linear Kernel ◽  
Characteristic Functional ◽  
Initial Space ◽  
Radon Probability Measure ◽  
Locally Convex

Abstract Problems of the Mackey-continuity of characteristic functionals and the localization of linear kernels of Radon probability measures in locally convex spaces are investigated. First the class of spaces is described, for which the continuity takes place. Then it is shown that in a non-complete sigmacompact inner product space, as well as in a non-complete sigma-compact metizable nuclear space, there may exist a Radon probability measure having a non-continuous characteristic functional in the Mackey topology and a linear kernel not contained in the initial space. Similar problems for moment forms and higher order kernels are also touched upon. Finally, a new proof of the result due to Chr. Borell is given, which asserts that any Gaussian Radon measure on an arbitrary Hausdorff locally convex space has the Mackey-continuous characteristic functional.

A Simons type integral inequality for closed submanifolds in the product space Sn×R

2021 ◽  
Vol 209 ◽  
pp. 112366
Author(s):  
Fábio R. dos Santos ◽  
Sylvia F. da Silva
Keyword(s):  
Integral Inequality ◽  
Product Space ◽  
Type Integral
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