Continuous selections on locally compact separable metric spaces

1970 ◽  
pp. 102-110 ◽  
Author(s):  
Gail S. Young
Keyword(s):  
Metric Spaces ◽  
Locally Compact ◽  
Continuous Selections

Nowhere Dense Subsets of Metric Spaces with Applications to Stone-Cech Compactifications

1972 ◽  
Vol 24 (4) ◽  
pp. 622-630 ◽  
Author(s):  
Jack R. Porter ◽  
R. Grant Woods
Keyword(s):  
Metric Space ◽  
Hausdorff Space ◽  
Metric Spaces ◽  
Dense Subset ◽  
Locally Compact ◽  
Completely Regular ◽  
Isolated Points ◽  
Remote Points ◽  
Topological Boundary ◽  
Regular Closed

Let X be a metric space. Assume either that X is locally compact or that X has no more than countably many isolated points. It is proved that if F is a nowhere dense subset of X, then it is regularly nowhere dense (in the sense of Katětov) and hence is contained in the topological boundary of some regular-closed subset of X. This result is used to obtain new properties of the remote points of the Stone-Čech compactification of a metric space without isolated points.Let βX denote the Stone-Čech compactification of the completely regular Hausdorff space X. Fine and Gillman [3] define a point p of βX to be remote if p is not in the βX-closure of a discrete subset of X.

Simple Links in Locally Compact Connected Hausdorff Spaces are Nondegenerate

1981 ◽  
Vol 34 (2) ◽  
pp. 349-355
Author(s):  
David John
Keyword(s):  
Hausdorff Space ◽  
Metric Spaces ◽  
Connected Space ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
Peano Continua

The fact that simple links in locally compact connected metric spaces are nondegenerate was probably first established by C. Kuratowski and G. T. Whyburn in [2], where it is proved for Peano continua. J. L. Kelley in [3] established it for arbitrary metric continua, and A. D. Wallace extended the theorem to Hausdorff continua in [4]. In [1], B. Lehman proved this theorem for locally compact, locally connected Hausdorff spaces. We will show that the locally connected property is not necessary.A continuum is a compact connected Hausdorff space. For any two points a and b of a connected space M, E(a, b) denotes the set of all points of M which separate a from b in M. The interval ab of M is the set E(a, b) ∪ {a, b}.

scholarly journals Hyperspaces of direct limits of locally compact metric spaces

1988 ◽  
Vol 29 (1) ◽  
pp. 55-60
Author(s):  
D.W. Curtis ◽  
D.S. Patching
Keyword(s):  
Metric Spaces ◽  
Locally Compact ◽  
Compact Metric Spaces ◽  
Direct Limits

scholarly journals Quantitative nonlinear embeddings into Lebesgue sequence spaces

2016 ◽  
Vol 08 (01) ◽  
pp. 117-150
Author(s):  
Florent P. Baudier
Keyword(s):  
Group Theory ◽  
Positive Solution ◽  
Metric Spaces ◽  
Exact Formula ◽  
Geometric Group Theory ◽  
Sequence Spaces ◽  
Text Compression ◽  
Property A ◽  
Locally Compact ◽  
Strong Embeddability

In this paper fundamental nonlinear geometries of Lebesgue sequence spaces are studied in their quantitative aspects. Applications of this work are a positive solution to the strong embeddability problem from [Formula: see text] into [Formula: see text] ([Formula: see text]) and new insights on the coarse embeddability problem from [Formula: see text] into [Formula: see text], [Formula: see text]. Relevant to geometric group theory purposes, the exact [Formula: see text]-compression of [Formula: see text] is computed. Finally coarse deformation of metric spaces with property A and locally compact amenable groups is investigated.

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 computably locally compact Hausdorff spaces

2009 ◽  
Vol 19 (1) ◽  
pp. 101-117
Author(s):  
YATAO XU ◽  
TANJA GRUBBA
Keyword(s):  
Metric Spaces ◽  
Euclidean Spaces ◽  
Hausdorff Spaces ◽  
Specific Kind ◽  
Locally Compact ◽  
Complete Investigation ◽  
Infinite Sequences ◽  
Compact Subsets

Locally compact Hausdorff spaces generalise Euclidean spaces and metric spaces from ‘metric’ to ‘topology’. But does the effectivity on the latter (Brattka and Weihrauch 1999; Weihrauch 2000) still hold for the former? In fact, some results will be totally changed. This paper provides a complete investigation of a specific kind of space – computably locally compact Hausdorff spaces. First we characterise this type of effective space, and then study computability on closed and compact subsets of them. We use the framework of the representation approach, TTE, where continuity and computability on finite and infinite sequences of symbols are defined canonically and transferred to abstract sets by means of notations and representations.

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