scholarly journals Moore-closed and first countable feebly compact extension spaces

1987 ◽  
Vol 27 (1) ◽  
pp. 11-28 ◽  
Author(s):  
R.M. Stephenson
Keyword(s):  
Extension Spaces ◽  
Compact Extension

Topologies of the Hyperspace which Are Induced by Extension Spaces

1984 ◽  
Vol 118 (1) ◽  
pp. 105-113 ◽  
Author(s):  
Hans-Jürgen Schmidt
Keyword(s):  
Extension Spaces

scholarly journals On pseudocompact topological Brandt λ0-extensions of semitopological monoids

2013 ◽  
Vol 1 ◽  
pp. 60-79
Author(s):  
Oleg Gutik ◽  
Kateryna Pavlyk
Keyword(s):  
Topological Properties ◽  
Countably Compact ◽  
Compact Extension

AbstractIn the paper we investigate topological properties of a topological Brandt λ0-extension B0λ(S) of a semitopological monoid S with zero. In particular we prove that for every Tychonoff pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) semitopological monoid S with zero there exists a unique semiregular pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) extension B0λ(S) of S and establish their Stone-Cˇ ech and Bohr compactifications. We also describe a category whose objects are ingredients in the constructions of pseudocompact (resp., countably compact, sequentially compact, compact) topological Brandt λ0- extensions of pseudocompact (resp., countably compact, sequentially compact, compact) semitopological monoids with zeros.

scholarly journals On compactification of mappings

1974 ◽  
Vol 19 (2) ◽  
pp. 105-108
Author(s):  
P. A. Firby
Keyword(s):  
Continuous Function ◽  
Dense Subspace ◽  
Compact Extension ◽  
Tychonoff Spaces ◽  
Function Mapping

If X and Y are Tychonoff spaces then the continuous function f mapping X onto Y is said to be compact (perfect, or proper) if it is closed and point inverses are compact. If h is a continuous function mapping X onto Y then by a compactification of h we mean a pair (X*, h*) where X* is Tychonoff and contains X as a dense subspace, and where h*: X*→Y is a compact extension of h. The idea of a mapping compactification first appeared in (7). In (1) it was shown that any compactification of X determines a compactification of h, and that any compactification of h can be determined in this way. This idea was then developed in (2) and (3).

scholarly journals Retracts and extension spaces for perfectly normal spaces.

1962 ◽  
Vol 9 (3) ◽  
pp. 193-197 ◽  
Author(s):  
Byron H. McCandless
Keyword(s):  
Extension Spaces ◽  
Perfectly Normal

scholarly journals Meromorphic extension spaces

1992 ◽  
Vol 42 (3) ◽  
pp. 501-515
Author(s):  
Le Mau Hai ◽  
Nguyen Van Khue
Keyword(s):  
Extension Spaces

scholarly journals A Characteristic Factor for the 3-Term IP Roth Theorem in $\mathbb{Z}_3^\mathbb{N}$

10.37236/3715 ◽  
2014 ◽  
Vol 21 (3) ◽  
Author(s):  
Randall McCutcheon ◽  
Alistair Windsor
Keyword(s):  
Characteristic Factor ◽  
Alpha Omega ◽  
Natural Inclusion ◽  
One Step ◽  
Compact Extension

Let $\Omega = \bigoplus_{i=1}^\infty \mathbb{Z}_3$ and $e_i = (0, \dots, 0 , 1, 0, \dots)$ where the $1$ occurs in the $i$-th coordinate. Let $\mathscr{F}=\{ \alpha \subset \mathbb{N} : \varnothing \neq \alpha, \alpha \text{ is finite} \}$. There is a natural inclusion of $\mathscr{F}$ into $\Omega$ where $\alpha \in \mathscr{F}$ is mapped to $e_\alpha = \sum_{i \in \alpha} e_i$. We give a new proof that if $E \subset \Omega$ with $d^*(E) >0$ then there exist $\omega \in \Omega$ and $\alpha \in \mathscr{F}$ such that \[ \{ \omega, \omega+ e_\alpha, \omega + 2 e_\alpha \} \subset E.\]Our proof establishes that for the ergodic reformulation of the problem there is a characteristic factor that is a one step compact extension of the Kronecker factor.

On the Katětov and Stone-Čech Extensions

1959 ◽  
Vol 2 (1) ◽  
pp. 1-4 ◽  
Author(s):  
Bernhard Banaschewski
Keyword(s):  
Compact Space ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Approximation Theorem ◽  
General Topology ◽  
Natural Question ◽  
Completely Regular ◽  
Extension Spaces ◽  
Weierstrass Approximation Theorem

In general topology, one knows several standard extension spaces defined for one class of spaces or another and it is a natural question concerning any two such extensions which are defined for the same space whether they can ever be equal to each other. In the following, this problem will be considered for the Stone-Čech compactification βE of a completely regular non-compact Hausdorff space E[4] and Katětov's maximal Hausdorff extension κE of E[5]. It will be shown that βEκE always holds or, what amounts to the same, that κE can never be compact. As an application of this it will be proved that any completely regular Hausdorff space is dense in some non-compact space in which the Stone-Weierstrass approximation theorem holds.

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