On $p$-sequential $p$-compact spaces

García-Ferreira, Salvador, and Tamariz-Mascarúa, Angel. "On $p$-sequential $p$-compact spaces." Commentationes Mathematicae Universitatis Carolinae 34.2 (1993): 347-356. <http://eudml.org/doc/247507>.

@article{García1993,
abstract = {It is shown that a space $X$ is $L(\{\}^\{\mu \}p)$-Weakly Fréchet-Urysohn for $p\in \omega ^\{\ast \}$ iff it is $L(\{\}^\{\nu \}p)$-Weakly Fréchet-Urysohn for arbitrary $\mu ,\nu <\omega _1$, where $\{\}^\{\mu \}p$ is the $\mu $-th left power of $p$ and $L(q)=\lbrace \{\}^\{\mu \}q:\mu <\omega _1\rbrace $ for $q\in \omega ^\{\ast \}$. We also prove that for $p$-compact spaces, $p$-sequentiality and the property of being a $L(\{\}^\{\nu \}p)$-Weakly Fréchet-Urysohn space with $\nu <\omega _1$, are equivalent; consequently if $X$ is $p$-compact and $\nu <\omega _1$, then $X$ is $p$-sequential iff $X$ is $\{\}^\{\nu \}p$-sequential (Boldjiev and Malyhin gave, for each $P$-point $p\in \omega ^\{\ast \}$, an example of a compact space $X_p$ which is $^2p$-Fréchet-Urysohn and it is not $p$-Fréchet-Urysohn. The question whether such an example exists in ZFC remains unsolved).},
author = {García-Ferreira, Salvador, Tamariz-Mascarúa, Angel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$p$-compact; $p$-sequential; $\operatorname\{FU\}(p)$-space; Rudin-Keisler order; tensor product of ultrafilters; left power of ultrafilters; $\operatorname\{SMU\}(M)$-space; $\operatorname\{WFU\}(M)$-space; -space; Rudin-Keisler order; tensor product of ultrafilters; left power of ultrafilters; -space; -space; Franklin space; -compact spaces; - sequentiality},
language = {eng},
number = {2},
pages = {347-356},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On $p$-sequential $p$-compact spaces},
url = {http://eudml.org/doc/247507},
volume = {34},
year = {1993},
}

TY - JOUR
AU - García-Ferreira, Salvador
AU - Tamariz-Mascarúa, Angel
TI - On $p$-sequential $p$-compact spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 2
SP - 347
EP - 356
AB - It is shown that a space $X$ is $L({}^{\mu }p)$-Weakly Fréchet-Urysohn for $p\in \omega ^{\ast }$ iff it is $L({}^{\nu }p)$-Weakly Fréchet-Urysohn for arbitrary $\mu ,\nu <\omega _1$, where ${}^{\mu }p$ is the $\mu $-th left power of $p$ and $L(q)=\lbrace {}^{\mu }q:\mu <\omega _1\rbrace $ for $q\in \omega ^{\ast }$. We also prove that for $p$-compact spaces, $p$-sequentiality and the property of being a $L({}^{\nu }p)$-Weakly Fréchet-Urysohn space with $\nu <\omega _1$, are equivalent; consequently if $X$ is $p$-compact and $\nu <\omega _1$, then $X$ is $p$-sequential iff $X$ is ${}^{\nu }p$-sequential (Boldjiev and Malyhin gave, for each $P$-point $p\in \omega ^{\ast }$, an example of a compact space $X_p$ which is $^2p$-Fréchet-Urysohn and it is not $p$-Fréchet-Urysohn. The question whether such an example exists in ZFC remains unsolved).
LA - eng
KW - $p$-compact; $p$-sequential; $\operatorname{FU}(p)$-space; Rudin-Keisler order; tensor product of ultrafilters; left power of ultrafilters; $\operatorname{SMU}(M)$-space; $\operatorname{WFU}(M)$-space; -space; Rudin-Keisler order; tensor product of ultrafilters; left power of ultrafilters; -space; -space; Franklin space; -compact spaces; - sequentiality
UR - http://eudml.org/doc/247507
ER -