منابع مشابه
Maximal (sequentially) compact topologies
We revisit the known problem whether each compact topology is contained in a maximal compact topology and collect some partial answers to this question. For instance we show that each compact topology is contained in a compact topology in which convergent sequences have unique limits. We also answer a question of D.E. Cameron by showing that each sequentially compact topology is contained in a ...
متن کاملCompact Group Topologies for R
There is a compact solenoidal group S that is group isomorphic to the additive real numbers R. The existence of 5 leads to a study of compact real groups; that is, compact groups which are group isomorphic to R. The compact real groups are characterized as products of 5. Various conditions on a topological group G are given which are equivalent to G being compact real. It is shown that any comp...
متن کاملOn Maximality of Compact Topologies
Using some advanced properties of the de Groot dual and some generalization of the Hofmann-Mislove theorem, we solve in the positive the question of D. E. Cameron: Is every compact topology contained in some maximal compact topology? Date: 29. 8. 2004. Last revision: 14. 10. 2004
متن کاملCertain Weakly Generated Noncompact, Pseudo-compact Topologies on Tychonoff Cubes
Given an uncountable cardinal א, the product space I, I = [0, 1], is called a Tychonoff cube. A collection of closed subsets of a subspace Y of a Tychonoff cube I that covers Y determines a weak topology for Y . The collection of compact subsets of I that have a countable dense subset covers I. It is known from work of the author and I. Ivanšić that the weak topology generated by this collectio...
متن کاملPseudocompact Group Topologies with No Infinite Compact Subsets
We show that every Abelian group satisfying a mild cardinal inequality admits a pseudocompact group topology from which all countable subgroups inherit the maximal totally bounded topology (we say that such a topology satisfies property ♯). This criterion is used in conjunction with an analysis of the algebraic structure of pseudocompact groups to obtain, under the Generalized Continuum Hypothe...
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ژورنال
عنوان ژورنال: Tamkang Journal of Mathematics
سال: 1993
ISSN: 2073-9826,0049-2930
DOI: 10.5556/j.tkjm.24.1993.4504