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dc.contributor.advisorTamano, Hisahiro
dc.contributor.authorMarrache, Nazem M.en_US
dc.date.accessioned2019-10-11T15:11:01Z
dc.date.available2019-10-11T15:11:01Z
dc.date.created1968en_US
dc.date.issued1968en_US
dc.identifieraleph-254935en_US
dc.identifier.urihttps://repository.tcu.edu/handle/116099117/33798
dc.description.abstractA topological space X is said to be an L-space if for each point x of X there is a collection, H = (H_alpha: alpha in A), of open sets and a compact set G such that: (1) x not in cl(H_alpha) for a in A, (2) H covers X - G, and (3) H is locally finite at each point of X - G. A space X is said to be k-countable if for each point x of X there is a sequence, {U_n} from n=1 to infinity, of neighborhoods of x such that the Intersection from n=1 to infinity of cl(U_n) is compact. The notion of L-space has the distinction of being a simultaneous generalization of the concepts of locally compact space, first countable space and k-countable space. Ernest Michael introduced the notions of r-space and of q-space each of which is a generalization of the concepts of locally compact and first countable space. The purpose of this dissertation is to study the properties of these spaces and to present some relations which exist among them. Specifically, the following theorems are proven. Theorem. If a space X is both an L-space and a q-space then X is a k-space. Theorem. If a space X is a k-countable q-space then X is both an r-space and a k-space. Theorem. A k-countable q-space is preserved under an open mapping. Theorem. The product space of two k-countable q-spaces is a k-countable q-space. Theorem. If X is a pseudo-compact L-space then X is a k-space. Theorem. If X is a pseudo-compact k-countable space then X is both an r-space and a k-space. Further, we show that the notion of L-space is sufficient to insure the pseudo-compactness of the product of two pseudo-compact spaces. It should be mentioned that pseudo-compactness which appeared in the above results has some interaction with these local properties. Finally, some local properties are discussed in terms of properties of compactifications.
dc.format.extentiii, 45 leaves, bounden_US
dc.format.mediumFormat: Printen_US
dc.language.isoengen_US
dc.relation.ispartofTexas Christian University dissertationen_US
dc.relation.ispartofAS38.M368en_US
dc.subject.lcshTopologyen_US
dc.titleCertain local properties of topological spacesen_US
dc.typeTexten_US
etd.degree.departmentDepartment of Mathematics
etd.degree.levelDoctoral
local.collegeCollege of Science and Engineering
local.departmentMathematics
local.academicunitDepartment of Mathematics
dc.type.genreDissertation
local.subjectareaMathematics
dc.identifier.callnumberMain Stacks: AS38 .M368 (Regular Loan)
dc.identifier.callnumberSpecial Collections: AS38 .M368 (Non-Circulating)
etd.degree.nameDoctor of Philosophy
etd.degree.grantorTexas Christian University


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