Linear subspace of Rl without dense totally disconnected subsets

Ciesielski, K.

Ciesielski, K.

Fundamenta Mathematicae, Tome 142 (1993), p. 85-88 / Harvested from The Polish Digital Mathematics Library

Résumé

In [1] the author showed that if there is a cardinal κ such that $2^{κ} = κ^{+}$ then there exists a completely regular space without dense 0-dimensional subspaces. This was a solution of a problem of Arkhangel’skiĭ. Recently Arkhangel’skiĭ asked the author whether one can generalize this result by constructing a completely regular space without dense totally disconnected subspaces, and whether such a space can have a structure of a linear space. The purpose of this paper is to show that indeed such a space can be constructed under the additional assumption that there exists a cardinal κ such that $2^{κ} = κ^{+}$ and $2^{κ^{+}} = κ^{+ +}$ .

Publié le : 1993-01-01

Zbl 0808.54024

EUDML-ID : urn:eudml:doc:211973

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     author = {K. Ciesielski},
     title = {Linear subspace of Rl without dense totally disconnected subsets},
     journal = {Fundamenta Mathematicae},
     volume = {142},
     year = {1993},
     pages = {85-88},
     zbl = {0808.54024},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv142i1p85bwm}
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Ciesielski, K. Linear subspace of Rl without dense totally disconnected subsets. Fundamenta Mathematicae, Tome 142 (1993) pp. 85-88. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv142i1p85bwm/

Bibliographie

[00000] [1] K. Ciesielski, L-space without any uncountable 0-dimensional subspace, Fund. Math. 125 (1985), 231-235. | Zbl 0589.54031

[00001] [2] R. Engelking, General Topology, Polish Scientific Publishers, Warszawa 1977.

[00002] [3] K. Kunen, Set Theory, North-Holland, 1983.