an:03883178
Zbl 0554.54009
Bell, Murray; Ginsburg, John
Compact spaces and spaces of maximal complete subgraphs
EN
Trans. Am. Math. Soc. 283, 329-338 (1984).
00147938
1984
j
54D30
space of all maximal complete subgraphs; binary subbase; zero-dimensional supercompact spaces
Let G be a graph and let M(G) denote the collection of all maximal complete subgraphs of G. The set M(G) is topologized by considering it to be a subspace of the power set of G equipped with the usual product topology. The main question is the following: Which compact spaces can be represented as M(G) for some graph G? The answer to this question is: precisely those that have a binary subbase for the closed sets consisting of clopen sets. An example is presented that this class of spaces does not coincide with the class of all zero-dimensional supercompact spaces.
J.van Mill