Local properties of topological spaces and remainders in compactifications

2019 ◽  
Vol 158 (2) ◽  
pp. 306-317
Author(s):  
A. V. Arhangel’skii
Keyword(s):  
Topological Spaces ◽  
Local Properties

Local properties of topological spaces

1954 ◽  
Vol 21 (1) ◽  
pp. 163-171 ◽  
Author(s):  
Ernest Michael
Keyword(s):  
Topological Spaces ◽  
Local Properties

scholarly journals The unions of dense metrizable subspaces with certain local properties

Filomat ◽  
2015 ◽  
Vol 29 (1) ◽  
pp. 83-88
Author(s):  
A.V. Arhangel’skii ◽  
S. Tokgöz
Keyword(s):  
Countable Family ◽  
Topological Spaces ◽  
Locally Compact ◽  
Tychonoff Space ◽  
Countable Collection ◽  
Local Properties ◽  
Separable Spaces

Many important examples of topological spaces can be represented as a union of a finite or countable collection of metrizable subspaces. However, it is far from clear which spaces in general can be obtained in this way. Especially interesting is the case when the subspaces are dense in the union. We present below several results in this direction. In particular, we show that if a Tychonoff space X is the union of a countable family of dense metrizable locally compact subspaces, then X itself is metrizable and locally compact. We also prove a similar result for metrizable locally separable spaces. Notice in this connection that the union of two dense metrizable subspaces needn?t be metrizable. Indeed, this is witnessed by a well-known space constructed by R.W. Heath.

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

Variation of the local properties in TmxSe (0.8 < x ≤ 1.0) : 169Tm Mössbauer and X-ray measurements

1982 ◽  
Vol 43 (6) ◽  
pp. 961-971 ◽  
Author(s):  
J.A. Hodges ◽  
G. Jéhanno ◽  
D. Debray ◽  
F. Holtzberg ◽  
M. Loewenhaupt
Keyword(s):  
X Ray ◽  
Local Properties
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