Open Access
M. Koçak, İ. Akça
Taiwanese J. Math. 11(1): 15-26 (2007). DOI: 10.11650/twjm/1500404630


If $X$ is a discrete topological space, the points of its Stone-Čech compactification $\beta X$ can be regarded as ultrafilters on $X$, and this fact is a useful tool in analysing the properties of $\beta X$. The purpose of this paper is to describe the compactification $\tilde{X}$ of a metric space in terms of the concept of near ultrafilters. We describe the topological space $\tilde{X}$ and we investigate conditions under which $\tilde{S}$ will be a semigroup compactification if $S$ is a semigroup which has a metric. These conditions will always hold if the topology of $S$ is defined by an invariant metric, and in this case our compactification $\tilde{S}$ coincides with $S^{LUC}$.


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M. Koçak. İ. Akça. "COMPACTIFICATIONS OF METRIC SPACES." Taiwanese J. Math. 11 (1) 15 - 26, 2007.


Published: 2007
First available in Project Euclid: 18 July 2017

zbMATH: 1139.54023
MathSciNet: MR2304001
Digital Object Identifier: 10.11650/twjm/1500404630

Primary: 32J05 , 54D35 , 54D60

Keywords: Compactifications , near ultrafilters , semigroup compactification

Rights: Copyright © 2007 The Mathematical Society of the Republic of China

Vol.11 • No. 1 • 2007
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