An abstract Kolmogorov theorem, and an application to metric spaces and topological groups

2018 ◽  
Vol 209 (11) ◽  
pp. 1575-1602
Author(s):  
S. V. Bochkarev
Keyword(s):  
Metric Spaces ◽  
Topological Groups ◽  
Kolmogorov Theorem

scholarly journals Spaces having no large dyadic subspace

1970 ◽  
Vol 2 (2) ◽  
pp. 261-265
Author(s):  
Jason Gait
Keyword(s):  
Metric Spaces ◽  
Topological Groups ◽  
Compact Metric Spaces ◽  
Interesting Corollary ◽  
Discrete Spaces ◽  
Continuous Images

Gillman-Henriksen have defined a class of spaces, containing the discrete spaces and their Stone-Čech compactifications, called F'-spaces. The dyadic spaces are the continuous images of products of finite discrete spaces – a class which contains the compact metric spaces and all compact topological groups. In this paper it is shown that F'-spaces have no infinite dyadic sutspaces and, almost always, no dyadic compactifications. An interesting corollary is that if βX \ X is dyadic, then X is pseudocompact.

scholarly journals Completeness and compactness properties in metric spaces, topological groups and function spaces

2017 ◽  
Vol 226 ◽  
pp. 134-164 ◽  
Author(s):  
Alejandro Dorantes-Aldama ◽  
Dmitri Shakhmatov
Keyword(s):  
Metric Spaces ◽  
Function Spaces ◽  
Topological Groups ◽  
And Function

scholarly journals The Riesz-Kolmogorov theorem on metric spaces

2014 ◽  
Vol 15 (2) ◽  
pp. 459 ◽  
Author(s):  
Przemysław Górka ◽  
Anna Macios
Keyword(s):  
Metric Spaces ◽  
Kolmogorov Theorem

Coarse Geometry of Topological Groups

2021 ◽  
Author(s):  
Christian Rosendal
Keyword(s):  
Geometric Structure ◽  
Metric Spaces ◽  
Automorphism Groups ◽  
Mathematical Practice ◽  
Worked Examples ◽  
Topological Groups ◽  
Diffeomorphism Groups ◽  
Locally Compact ◽  
Open Problems ◽  
Topological Transformation

This book provides a general framework for doing geometric group theory for many non-locally-compact topological transformation groups that arise in mathematical practice, including homeomorphism and diffeomorphism groups of manifolds, isometry groups of separable metric spaces and automorphism groups of countable structures. Using Roe's framework of coarse structures and spaces, the author defines a natural coarse geometric structure on all topological groups. This structure is accessible to investigation, especially in the case of Polish groups, and often has an explicit description, generalising well-known structures in familiar cases including finitely generated discrete groups, compactly generated locally compact groups and Banach spaces. In most cases, the coarse geometric structure is metrisable and may even be refined to a canonical quasimetric structure on the group. The book contains many worked examples and sufficient introductory material to be accessible to beginning graduate students. An appendix outlines several open problems in this young and rich theory.

Kolmogorov’s abstract theorem: Application to metric spaces and topological groups

2015 ◽  
Vol 91 (3) ◽  
pp. 367-370 ◽  
Author(s):  
S. V. Bochkarev
Keyword(s):  
Metric Spaces ◽  
Topological Groups ◽  
Abstract Theorem

Crystallography in two-dimensional metric spaces*

1969 ◽  
Vol 130 (1-6) ◽  
pp. 277-303 ◽  
Author(s):  
Aloysio Janner ◽  
Edgar Ascher
Keyword(s):  
Metric Spaces ◽  
Two Dimensional

Convergence and Stability For Ishikawa Iterative Scheme in Convex Metric Spaces

2011 ◽  
Vol 4 (6) ◽  
pp. 341-343
Author(s):  
Aarti Kadian ◽  
◽  
Alok Kumar
Keyword(s):  
Metric Spaces ◽  
Iterative Scheme ◽  
Convergence And Stability ◽  
Convex Metric Spaces

Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

2016 ◽  
Vol 2017 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Muhammad Usman Ali ◽  
◽  
Tayyab Kamran ◽  
Mihai Postolache ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Integral Inclusion

ON THE QUANTIFICATION OF UNIFORM PROPERTIES.PART 2

2001 ◽  
Vol 37 (1-2) ◽  
pp. 169-184
Author(s):  
B. Windels
Keyword(s):  
Metric Spaces ◽  
Uniform Spaces ◽  
Complete Metric Spaces ◽  
The Subject

In 1930 Kuratowski introduced the measure of non-compactness for complete metric spaces in order to measure the discrepancy a set may have from being compact.Since then several variants and generalizations concerning quanti .cation of topological and uniform properties have been studied.The introduction of approach uniform spaces,establishes a unifying setting which allows for a canonical quanti .cation of uniform concepts,such as completeness,which is the subject of this article.

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