On Weaker Forms of Paracompactness, Countable Compactness, and Lindelöfness
| Autor: | T. R. Hamlett, Dragan Jankovic |
|---|---|
| Rok vydání: | 1994 |
| Předmět: |
Ideal (set theory)
General Neuroscience Hausdorff space Mathematics::General Topology Totally bounded space Topological space Space (mathematics) General Biochemistry Genetics and Molecular Biology Combinatorics Mathematics::Logic Compact space History and Philosophy of Science Bounded function Paracompact space Mathematics |
| Zdroj: | Annals of the New York Academy of Sciences. 728:41-49 |
| ISSN: | 0077-8923 |
| DOI: | 10.1111/j.1749-6632.1994.tb44132.x |
| Popis: | An ideal on a set X is a nonempty collection of subsets closed under the operations of finite union and subset. The concepts of parabounded and countably bounded subsets are defined as well as regularity with respect to an ideal I(i.e., I-regular). The bounded subsets of a topological space are characterized as the subsets which are both parabounded and countably bounded. It is shown that if (X, τ) is a Hausdorff space and I is an ideal on X such that I∩τ={O}, then (X, τ) is compact modulo I iff (X, τ) is H-closed and I-regular. Examples are given which place e-Lindelofness in the hierarchy of known properties and it is shown that para-Lindelof e-Lindelof spaces are Lindelof. It is shown that in the category of Hausdorff spaces, perfect images of e-paracompact spaces are e-paracompact. Posed as an open question is the following: What can be said about the closed continuous image of an e-paracompact space? |
| Databáze: | OpenAIRE |
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