scholarly journals Locally bounded spaces

1975 ◽  
Vol 19 (4) ◽  
pp. 321-325 ◽  
Author(s):  
P. Th. Lambrinos
Keyword(s):  
Compact Sets ◽  
Local Compactness ◽  
Compact Neighbourhood ◽  
Neighbourhood Basis

The three common definitions of local compactness require, respectively, each point to have a compact neighbourhood, a neighbourhood basis consisting of compact sets, or a closed compact neighbourhood. These definitions are equivalent in Hausdorff or in regular spaces but not in general (3, 7).

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

ON THREADING CONTINUOUS FUNCTIONS THROUGH COMPACT SETS

1982 ◽  
Vol 8 (2) ◽  
pp. 455
Author(s):  
Akemann ◽  
Bruckner
Keyword(s):  
Continuous Functions ◽  
Compact Sets

A Weak Hadamard Smooth Renorming of L1(Ω, μ)

1993 ◽  
Vol 36 (4) ◽  
pp. 407-413 ◽  
Author(s):  
Jonathan M. Borwein ◽  
Simon Fitzpatrick
Keyword(s):  
Compact Sets ◽  
Weakly Compact ◽  
Weakly Compact Sets

AbstractWe show that L1(μ) has a weak Hadamard differential)le renorm (i.e. differentiable away from the origin uniformly on all weakly compact sets) if and only if μ is sigma finite. As a consequence several powerful recent differentiability theorems apply to subspaces of L1.

Weakly compact sets in L∞(μ,E)

2012 ◽  
Vol 263 (4) ◽  
pp. 1098-1102
Author(s):  
Surjit Singh Khurana
Keyword(s):  
Compact Sets ◽  
Weakly Compact ◽  
Weakly Compact Sets

scholarly journals Local compactness in approach spaces II

2003 ◽  
Vol 2003 (2) ◽  
pp. 109-117
Author(s):  
R. Lowen ◽  
C. Verbeeck
Keyword(s):  
Stability Properties ◽  
Local Compactness ◽  
The Stability ◽  
Approach Spaces

This paper studies the stability properties of the concepts of local compactness introduced by the authors in 1998. We show that all of these concepts are stable for contractive, expansive images and for products.

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