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## Fundamenta Mathematicae

1993 | 142 | 1 | 85-88
Tytuł artykułu

### Linear subspace of Rl without dense totally disconnected subsets

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EN
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'ski{ĭ}. 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 $2^{κ^+}=κ^{++}$.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
85-88
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-03-31
poprawiono
1992-09-02
Twórcy
autor
• Department of Mathematics, West Virginia, University Morgantown, West Virginia 26506-6310, U.S.A.
Bibliografia
• [1] K. Ciesielski, L-space without any uncountable 0-dimensional subspace, Fund. Math. 125 (1985), 231-235.
• [2] R. Engelking, General Topology, Polish Scientific Publishers, Warszawa 1977.
• [3] K. Kunen, Set Theory, North-Holland, 1983.
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Bibliografia
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