Linear subspace of Rl without dense totally disconnected subsets
Fundamenta Mathematicae, Tome 142 (1993) no. 1, pp. 85-88
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 $2^{κ^+}=κ^{++}$.
@article{10_4064_fm_142_1_85_88,
author = {K. Ciesielski},
title = {Linear subspace of {Rl} without dense totally disconnected subsets},
journal = {Fundamenta Mathematicae},
pages = {85--88},
year = {1993},
volume = {142},
number = {1},
doi = {10.4064/fm-142-1-85-88},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-142-1-85-88/}
}
TY - JOUR AU - K. Ciesielski TI - Linear subspace of Rl without dense totally disconnected subsets JO - Fundamenta Mathematicae PY - 1993 SP - 85 EP - 88 VL - 142 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4064/fm-142-1-85-88/ DO - 10.4064/fm-142-1-85-88 LA - en ID - 10_4064_fm_142_1_85_88 ER -
K. Ciesielski. Linear subspace of Rl without dense totally disconnected subsets. Fundamenta Mathematicae, Tome 142 (1993) no. 1, pp. 85-88. doi: 10.4064/fm-142-1-85-88
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