scholarly journals Metric Compactifications and Coarse Structures

2015 ◽  
Vol 67 (5) ◽  
pp. 1091-1108 ◽  
Author(s):  
Kotaro Mine ◽  
Atsushi Yamashita
Keyword(s):  
Compact Space ◽  
Metric Spaces ◽  
Locally Compact ◽  
Totally Bounded ◽  
Compact Metric Spaces ◽  
Locally Compact Space ◽  
Equivalence Of Categories ◽  
Metrizable Spaces ◽  
Coarse Structures ◽  
Higson Corona

AbstractLet TB be the category of totally bounded, locally compact metric spaces with the C0 coarse structures. We show that if X and Y are in TB, then X and Y are coarsely equivalent if and only if their Higson coronas are homeomorphic. In fact, the Higson corona functor gives an equivalence of categories TB → K, where K is the category of compact metrizable spaces. We use this fact to show that the continuously controlled coarse structure on a locally compact space X induced by some metrizable compactification is determined only by the topology of the remainder .

On Unsymmetric Dirichlet Forms

1973 ◽  
Vol 25 (2) ◽  
pp. 252-260 ◽  
Author(s):  
Joanne Elliott
Keyword(s):  
Compact Space ◽  
Measure Space ◽  
Closed Subspace ◽  
Finite Measure ◽  
Dirichlet Forms ◽  
Locally Compact ◽  
Locally Compact Space ◽  
Finite Measure Space

Let F be a linear, but not necessarily closed, subspace of L2[X, dm], where (X,,m) is a σ-finite measure space with the Borel subsets of the locally compact space X. If u and v are measureable functions, then v is called a normalized contraction of u if and Assume that F is stable under normalized contractions, that is, if u ∈ F and v is a normalized contraction of u, then v ∈ F.

Actions That Fiber and Vector Semigroups

1972 ◽  
Vol 24 (1) ◽  
pp. 29-37 ◽  
Author(s):  
T. H. McH. Hanson
Keyword(s):  
Compact Space ◽  
Lie Group ◽  
Fiber Bundle ◽  
Closed Subset ◽  
Locally Compact ◽  
Locally Compact Space

From [2], we can derive a criterion for determining when an action of a Lie group on a locally compact space leads to a fiber bundle. Here, we present an equivalent criterion which can be stated purely in the language of actions of groups on spaces. This is Theorem I. Using this result, we are able to give a version of a result of Home [1] for dimensions greater than one. This is done in Theorem IV and Corollary IVA. In Theorem II, we show that if a vector semigroup acts on a space X, then whenever the map t ↦ tx is 1 — 1 from onto x, it is in fact a homeomorphism. Also, is a closed subset of X. This is also a version of a result in [1].

scholarly journals Quantum locally compact metric spaces

2013 ◽  
Vol 264 (1) ◽  
pp. 362-402 ◽  
Author(s):  
Frédéric Latrémolière
Keyword(s):  
Metric Spaces ◽  
Locally Compact ◽  
Compact Metric Spaces

ON ALGEBRAIC EQUATION WITH COEFFICIENTS FROM THE $ \beta $-UNIFORM ALGEBRA $ C_{\beta} (\Omega) $

2018 ◽  
Vol 52 (3 (247)) ◽  
pp. 161-165
Author(s):  
A.H. Kamalyan ◽  
M.I. Karakhanyan
Keyword(s):  
Algebraic Equation ◽  
Compact Space ◽  
Uniform Algebra ◽  
Locally Compact ◽  
Locally Compact Space

In this work the question of algebraic closeness of $ \beta $-uniform algebra $ A (\Omega) $ defined on locally compact space $ \Omega $ is investigated.

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