# Maximal nowhere dense $P$-sets in basically disconnected spaces and $F$-spaces

Andrey V. Koldunov; Aleksandr I. Veksler

Commentationes Mathematicae Universitatis Carolinae (2001)

- Volume: 42, Issue: 2, page 363-378
- ISSN: 0010-2628

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topKoldunov, Andrey V., and Veksler, Aleksandr I.. "Maximal nowhere dense $P$-sets in basically disconnected spaces and $F$-spaces." Commentationes Mathematicae Universitatis Carolinae 42.2 (2001): 363-378. <http://eudml.org/doc/248818>.

@article{Koldunov2001,

abstract = {In [5] the following question was put: are there any maximal n.d. sets in $\omega ^*$? Already in [9] the negative answer (under MA) to this question was obtained. Moreover, in [9] it was shown that no $P$-set can be maximal n.d. In the present paper the notion of a maximal n.d. $P$-set is introduced and it is proved that under CH there is no such a set in $\omega ^*$. The main results are Theorem 1.10 and especially Theorem 2.7(ii) (with Example in Section 3) in which the problem of the existence of maximal n.d. $P$-sets in basically disconnected compact spaces with rich families of n.d. $P$-sets is actually solved.},

author = {Koldunov, Andrey V., Veksler, Aleksandr I.},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {maximal n.d. set; $P$-set; maximal n.d. $P$-set; compact space; basically disconnected space; $F$-space; nowhere dense set; -set; compact space; basically disconnected; -space},

language = {eng},

number = {2},

pages = {363-378},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Maximal nowhere dense $P$-sets in basically disconnected spaces and $F$-spaces},

url = {http://eudml.org/doc/248818},

volume = {42},

year = {2001},

}

TY - JOUR

AU - Koldunov, Andrey V.

AU - Veksler, Aleksandr I.

TI - Maximal nowhere dense $P$-sets in basically disconnected spaces and $F$-spaces

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2001

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 42

IS - 2

SP - 363

EP - 378

AB - In [5] the following question was put: are there any maximal n.d. sets in $\omega ^*$? Already in [9] the negative answer (under MA) to this question was obtained. Moreover, in [9] it was shown that no $P$-set can be maximal n.d. In the present paper the notion of a maximal n.d. $P$-set is introduced and it is proved that under CH there is no such a set in $\omega ^*$. The main results are Theorem 1.10 and especially Theorem 2.7(ii) (with Example in Section 3) in which the problem of the existence of maximal n.d. $P$-sets in basically disconnected compact spaces with rich families of n.d. $P$-sets is actually solved.

LA - eng

KW - maximal n.d. set; $P$-set; maximal n.d. $P$-set; compact space; basically disconnected space; $F$-space; nowhere dense set; -set; compact space; basically disconnected; -space

UR - http://eudml.org/doc/248818

ER -

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