On $p$-sequential $p$-compact spaces
García-Ferreira, Salvador ; Tamariz-Mascarúa, Angel
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993), p. 347-356 / Harvested from Czech Digital Mathematics Library
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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 $L(q)=\{{}^{\mu }q:\mu <\omega _1\}$ 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).

Publié le : 1993-01-01
Classification:  03E05,  04A20,  54A25,  54D55 
@article{118587,
     author = {Salvador Garc\'\i a-Ferreira and Angel Tamariz-Mascar\'ua},
     title = {On $p$-sequential $p$-compact spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {34},
     year = {1993},
     pages = {347-356},
     zbl = {0791.54034},
     mrnumber = {1241743},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118587}
}

García-Ferreira, Salvador; Tamariz-Mascarúa, Angel. On $p$-sequential $p$-compact spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 347-356. http://gdmltest.u-ga.fr/item/118587/

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