Extension Closed and Cluster Closed Subspaces
Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1132-1136
Voir la notice de l'article provenant de la source Cambridge University Press
One of the most useful properties of a compact Hausdorff space is that such a space is closed whenever embedded into a Hausdorff space. This property does not extend to compact spaces with respect to embeddings into arbitrary spaces. Thus, an interesting topological problem is to characterize the types of absolute “closure” properties that are possessed by compact spaces. This is the problem that is solved in the present paper.The following notation and terminology will be used below. We shall consider a fixed space X and subspace A, representing arbitrary nonempty open subsets of X (respectively A ) by W (respectively V).
Harris, Douglas. Extension Closed and Cluster Closed Subspaces. Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1132-1136. doi: 10.4153/CJM-1972-119-8
@article{10_4153_CJM_1972_119_8,
author = {Harris, Douglas},
title = {Extension {Closed} and {Cluster} {Closed} {Subspaces}},
journal = {Canadian journal of mathematics},
pages = {1132--1136},
year = {1972},
volume = {24},
number = {6},
doi = {10.4153/CJM-1972-119-8},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-119-8/}
}
[1] 1. Douglas, Harris, Douglas, Harris, Structures in topology, Mem. Amer. Math. Soc, No. 115. Google Scholar
[2] 2. Douglas, Harris, Compact spaces and products of finite spaces, Proc. Amer. Math. Soc. 35 (1972), 275–280. Google Scholar
[3] 3. Douglas, Harris, Universal compact T1 spaces (to appear in General Topology and Appl.). Google Scholar
Cité par Sources :