Properties of cocontinuous functions and cocompact spaces
| dc.contributor.author | Francis, Gerald L. | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2017-01-30T21:23:40Z | en |
| dc.date.available | 2017-01-30T21:23:40Z | en |
| dc.date.issued | 1973 | en |
| dc.description.abstract | In this paper we study the concept of cotopology in the areas of cocon·tinuous functions and cocompact spaces. Initially we investigate and provide needed results concerning closed bases for a topological space. We then study cocontinuous functions by relating them to various other weaker forms of continuous functions, namely c-continuous, almost continuous and weakly continuous. We show that if (Y,U) is locally compact T₂, then f:(X,T)-->(Y,U) is cocontinuous if and only if f⁻¹(0) ε T for every 0 ε U such that (Y - 0) is compact. We note that every almost continuous function is cocontinuous, and we provide conditions under which a weakly continuous function is cocontinuous. We also show that a cocontinuous function from a saturated space to a regular space is continuous. In the area of cocompact spaces we first provide a partial answer to a question of J. M. Aarts as to when the union of cocompact subsets of a space is cocompact. We show that the union of a closed cocompact subset and a closed compact subset is cocompact. We then introduce the properties, locally cocompact and somewhere cocompact, and relate them to property L which was introduced by R. McCoy. We show that every somewhere cocompact regular space has property L, and that every locally cocompact regular space has property L locally. We provide examples to show that neither cocompact nor locally cocompact is equivalent to property L. | en |
| dc.description.degree | Ph. D. | en |
| dc.format.extent | iii, 78 leaves. | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.uri | http://hdl.handle.net/10919/74672 | en |
| dc.language.iso | en_US | en |
| dc.publisher | Virginia Polytechnic Institute and State University | en |
| dc.relation.isformatof | OCLC# 22409151 | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.lcc | LD5655.V856 1973.F7 | en |
| dc.subject.lcsh | Functions, Continuous | en |
| dc.subject.lcsh | Compact spaces | en |
| dc.title | Properties of cocontinuous functions and cocompact spaces | en |
| dc.type | Dissertation | en |
| dc.type.dcmitype | Text | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | doctoral | en |
| thesis.degree.name | Ph. D. | en |
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