Linear subspace of Rl without dense totally disconnected subsets

Ciesielski, K.. "Linear subspace of Rl without dense totally disconnected subsets." Fundamenta Mathematicae 142.1 (1993): 85-88. <http://eudml.org/doc/211973>.

@article{Ciesielski1993,
abstract = {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 $2^\{κ^+\}=κ^\{++\}$.},
author = {Ciesielski, K.},
journal = {Fundamenta Mathematicae},
keywords = {completely regular space; dense totally disconnected subspaces},
language = {eng},
number = {1},
pages = {85-88},
title = {Linear subspace of Rl without dense totally disconnected subsets},
url = {http://eudml.org/doc/211973},
volume = {142},
year = {1993},
}

TY - JOUR
AU - Ciesielski, K.
TI - Linear subspace of Rl without dense totally disconnected subsets
JO - Fundamenta Mathematicae
PY - 1993
VL - 142
IS - 1
SP - 85
EP - 88
AB - 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 $2^{κ^+}=κ^{++}$.
LA - eng
KW - completely regular space; dense totally disconnected subspaces
UR - http://eudml.org/doc/211973
ER -