Measures on countable product spaces

AbstractWe introduce the concept of a family of sets generating another family. Then we prove that if X is a topological space and X has W = {W(x): x ∈ X} which is finitely generated by a countable family satisfying (F) which consists of families each Noetherian of ω-rank, then X is metaLindelöf as well as a countable product of them. We also prove that if W satisfies ω-rank (F) and, for every x ∈ X, W(x) is of the form W 0(x) ∪ W 1(x), where W 0(x) is Noetherian and W 1(x) consists of neighbourhoods of x, then X is metacompact.

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Two preservation results for countable products of sequential spaces

Mathematical Structures in Computer Science ◽

10.1017/s0960129506005895 ◽

2007 ◽

Vol 17 (1) ◽

pp. 161-172 ◽

Cited By ~ 3

Author(s):

MATTHIAS SCHRÖDER ◽

ALEX SIMPSON

Keyword(s):

Topological Spaces ◽

Product Spaces ◽

Convergence Spaces ◽

Countable Product ◽

Discrete Spaces ◽

Sequential Spaces

We prove two results for the sequential topology on countable products of sequential topological spaces. First we show that a countable product of topological quotients yields a quotient map between the product spaces. Then we show that the reflection from sequential spaces to its subcategory of monotone ω-convergence spaces preserves countable products. These results are motivated by applications to the modelling of computation on non-discrete spaces.

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The Integral Over Product Spaces, and Wiener's Formula

Real Analysis Exchange ◽

10.2307/44152161 ◽

1991 ◽

Vol 17 (1) ◽

pp. 21

Author(s):

Henstock

Keyword(s):

Product Spaces

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Embeddedness, convexity, and rigidity of hypersurfaces in product spaces

Annals of Global Analysis and Geometry ◽

10.1007/s10455-020-09745-2 ◽

2021 ◽

Author(s):

Ronaldo Freire de Lima

Keyword(s):

Product Spaces

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Fuzzy Inner Product Space: Literature Review and a New Approach

Mathematics ◽

10.3390/math9070765 ◽

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.

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