Spaces which Cannot be Written as a Countable Disjoint Union of Closed Subsets
Canadian mathematical bulletin, Tome 16 (1973) no. 3, pp. 435-437
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It is well known (see [3](1)) that no continuum (i.e. compact, connected, Hausdorff space) can be written as a countable disjoint union of its (nonvoid) closed subsets. This result can be generalized in two ways into the setting of locally compact, connected, Hausdorff spaces. Using the one point compactification of a locally compact, connected, Hausdorff space X one can easily show that X cannot be written as a countable disjoint union of compact subsets. If one makes the further assumption that X is locally connected, then one can show that X cannot be written as a countable disjoint union of closed subsets.(2)
Eberhart, C.; Fugate, J. B.; Mohler, L. Spaces which Cannot be Written as a Countable Disjoint Union of Closed Subsets. Canadian mathematical bulletin, Tome 16 (1973) no. 3, pp. 435-437. doi: 10.4153/CMB-1973-069-1
@article{10_4153_CMB_1973_069_1,
author = {Eberhart, C. and Fugate, J. B. and Mohler, L.},
title = {Spaces which {Cannot} be {Written} as a {Countable} {Disjoint} {Union} of {Closed} {Subsets}},
journal = {Canadian mathematical bulletin},
pages = {435--437},
year = {1973},
volume = {16},
number = {3},
doi = {10.4153/CMB-1973-069-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1973-069-1/}
}
TY - JOUR AU - Eberhart, C. AU - Fugate, J. B. AU - Mohler, L. TI - Spaces which Cannot be Written as a Countable Disjoint Union of Closed Subsets JO - Canadian mathematical bulletin PY - 1973 SP - 435 EP - 437 VL - 16 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1973-069-1/ DO - 10.4153/CMB-1973-069-1 ID - 10_4153_CMB_1973_069_1 ER -
%0 Journal Article %A Eberhart, C. %A Fugate, J. B. %A Mohler, L. %T Spaces which Cannot be Written as a Countable Disjoint Union of Closed Subsets %J Canadian mathematical bulletin %D 1973 %P 435-437 %V 16 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1973-069-1/ %R 10.4153/CMB-1973-069-1 %F 10_4153_CMB_1973_069_1
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