Strong pseudocompact properties
Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 1, pp. 101-109
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library
For a free ultrafilter $p$ on $\mathbb{N}$,
the concepts of strong pseudocompactness,
strong $p$-pseudocompactness and
pseudo-$\omega$-boundedness were
introduced in [Angoa J., Ortiz-Castillo Y.F.,
Tamariz-Mascarúa A., Ultrafilters and
properties related to compactness,
Topology Proc. 43 (2014), 183--200]
and [García-Ferreira S., Ortiz-Castillo Y.F.,
Strong pseudocompact properties of
certain subspaces of $\mathbb N^*$,
submitted]. These properties in a space
$X$ characterize the pseudocompactness
of the hyperspace $\mathcal{K}(X)$ of
compact subsets of $X$ with the Vietoris
topology. In this paper, we study the
strong pseudocompactness and strong
$p$-pseudocompactness of certain spaces.
Besides, we established a relationship
between these kind of properties and
a result involving topological groups
of I. Protasov [Discrete subsets of
topological groups, Math. Notes 55
(1994), no. 1--2, 101--102].
For a free ultrafilter $p$ on $\mathbb{N}$,
the concepts of strong pseudocompactness,
strong $p$-pseudocompactness and
pseudo-$\omega$-boundedness were
introduced in [Angoa J., Ortiz-Castillo Y.F.,
Tamariz-Mascarúa A., Ultrafilters and
properties related to compactness,
Topology Proc. 43 (2014), 183--200]
and [García-Ferreira S., Ortiz-Castillo Y.F.,
Strong pseudocompact properties of
certain subspaces of $\mathbb N^*$,
submitted]. These properties in a space
$X$ characterize the pseudocompactness
of the hyperspace $\mathcal{K}(X)$ of
compact subsets of $X$ with the Vietoris
topology. In this paper, we study the
strong pseudocompactness and strong
$p$-pseudocompactness of certain spaces.
Besides, we established a relationship
between these kind of properties and
a result involving topological groups
of I. Protasov [Discrete subsets of
topological groups, Math. Notes 55
(1994), no. 1--2, 101--102].
Classification :
54A20, 54D30, 54D80, 54D99
Keywords: $p$-pseudocompactness; ultrapseudocompactness; strongly pseudocompactness; strongly $p$-pseudocompactness; weak $P$-points; $\mathfrak{c}-OK$ points; Rudin-Keisler pre-order
Keywords: $p$-pseudocompactness; ultrapseudocompactness; strongly pseudocompactness; strongly $p$-pseudocompactness; weak $P$-points; $\mathfrak{c}-OK$ points; Rudin-Keisler pre-order
@article{CMUC_2014_55_1_a7,
author = {Garc{\'\i}a-Ferreira, S. and Ortiz-Castillo, Y. F.},
title = {Strong pseudocompact properties},
journal = {Commentationes Mathematicae Universitatis Carolinae},
pages = {101--109},
year = {2014},
volume = {55},
number = {1},
mrnumber = {3160828},
zbl = {06383787},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMUC_2014_55_1_a7/}
}
García-Ferreira, S.; Ortiz-Castillo, Y. F. Strong pseudocompact properties. Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 1, pp. 101-109. http://geodesic.mathdoc.fr/item/CMUC_2014_55_1_a7/