tychonoff theorem
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Topology

2021 ◽  
pp. 126-144
Author(s):  
James Davidson
Keyword(s):  
Topological Spaces ◽  
Product Spaces ◽  
Product Topology ◽  
Weak Topologies ◽  
Tychonoff Theorem

This chapter discusses topological spaces and associated concepts, including first‐ and second‐countability, compactness, and separation properties. Weak topologies are defined. Product spaces, the product topology, and the Tychonoff theorem are treated and also ideas of embedding, compactification, and metrization.

scholarly journals Fuzzy Zorn’s lemma with applications

2021 ◽  
Vol 36 (4) ◽  
pp. 521-536
Author(s):  
Xiao-long Xin ◽  
Yu-long Fu
Keyword(s):  
Commutative Ring ◽  
Maximal Ideal ◽  
Prime Ideals ◽  
Nilpotent Elements ◽  
Fuzzy Ideal ◽  
Tychonoff Theorem

AbstractWe introduced the fuzzy axioms of choice, fuzzy Zorn’s lemma and fuzzy well-ordering principle, which are the fuzzy versions of the axioms of choice, Zorn’s lemma and well-ordering principle, and discussed the relations among them. As an application of fuzzy Zorn’s lemma, we got the following results: (1) Every proper fuzzy ideal of a ring was contained in a maximal fuzzy ideal. (2) Every nonzero ring contained a fuzzy maximal ideal. (3) Introduced the notion of fuzzy nilpotent elements in a ring R, and proved that the intersection of all fuzzy prime ideals in a commutative ring R is the union of all fuzzy nilpotent elements in R. (4) Proposed the fuzzy version of Tychonoff Theorem and by use of fuzzy Zorn’s lemma, we proved the fuzzy Tychonoff Theorem.

scholarly journals On measures of parameterized fuzzy compactness

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 2927-2938
Author(s):  
Vildan Çetkin
Keyword(s):  
Topological Space ◽  
Soft Set ◽  
General Topology ◽  
Fuzzy Soft Set ◽  
The Given ◽  
Tychonoff Theorem ◽  
Soft Topological Space

In the present study, the parameterized degree of compactness of a lattice valued fuzzy soft set is described in a fuzzy soft topological space. The extended versions of the basic compactness properties known in general topology are investigated for the given notion and some further characterizations of parameterized degree of fuzzy compactness are specified. In addition, a generalized version of Tychonoff Theorem is proved in the product fuzzy soft topological space.

Generalized Tychonoff theorem in L-fuzzy supratopological spaces1

2019 ◽  
Vol 36 (6) ◽  
pp. 6663-6668
Author(s):  
Hu Zhao ◽  
Gui-Xiu Chen ◽  
Hong-Ying Zhang
Keyword(s):  
Tychonoff Theorem

scholarly journals Compactness in MV-topologies: Tychonoff theorem and Stone–Čech compactification

2019 ◽  
Vol 59 (1-2) ◽  
pp. 57-79 ◽  
Author(s):  
Luz Victoria De La Pava ◽  
Ciro Russo
Keyword(s):  
Tychonoff Theorem

The Tychonoff theorem and invariant pseudodistances

2019 ◽  
Vol 10 (2) ◽  
pp. 284-290
Author(s):  
Tadeusz Kuczumow ◽  
Stanisław Prus
Keyword(s):  
Tychonoff Theorem

scholarly journals Fuzzy Soft Compact Topological Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Seema Mishra ◽  
Rekha Srivastava
Keyword(s):  
Topological Spaces ◽  
Fuzzy Topological Spaces ◽  
Tychonoff Theorem

In this paper, we have studied compactness in fuzzy soft topological spaces which is a generalization of the corresponding concept by R. Lowen in the case of fuzzy topological spaces. Several basic desirable results have been established. In particular, we have proved the counterparts of Alexander’s subbase lemma and Tychonoff theorem for fuzzy soft topological spaces.

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