Concerning R.L. Moore's axiom 5₁

dc.contributor.advisorMoore, R. L. (Robert Lee), 1882-
dc.creatorJones, F. Burton
dc.date.accessioned2018-08-06T14:42:17Z
dc.date.available2018-08-06T14:42:17Z
dc.date.issued1935
dc.descriptionIn any space satisfying Axioms 0, 1, 2, 3, 4, and 5 of R.L. Moore's Foundations of Point Set Theory a large body of Plane Analysis Situs theorems hold true. Nevertheless, not every such space is a subset of the plane even if completely separable. However, Moore has shown that if such a space satisfies certain additional axioms, it is a subset of a plane. This problem has also been studied by Leo Zippin and, more recently, by J.H. Roberts. In this paper the problem is again attacked, and the treatment emphasizes the rather peculiar role played by connectedness. As a matter of fact, connectedness enters into all of the axioms used by the author except Axioms 0, 1, and 6. In Part I a certain space is studied which, although not necessarily a subset of a plane, nevertheless, possesses many of the properties of a plane. However, if the space of Part I is completely separable or metric, it is shown to be a subset of a plane or a sphere. Definitions of terms peculiar to the treatment are given in the text. For the definition of terms not defined, the reader is refered to R.L. Moore's Foundations of Point Set Theory. Many of the notational conventions of this work are also used here without explanation.
dc.description.departmentMathematicsen_US
dc.format.mediumelectronicen_US
dc.identifierdoi:10.15781/T26D5PV5V
dc.identifier.urihttp://hdl.handle.net/2152/65948
dc.language.isoengen_US
dc.relation.ispartofUT Electronic Theses and Dissertationsen_US
dc.rightsCopyright © is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.en_US
dc.rights.restrictionOpenen_US
dc.subject.lcshMoore, R. L. (Robert Lee), 1882- Foundations of point set theory
dc.subject.lcshPoint set theory
dc.titleConcerning R.L. Moore's axiom 5₁en_US
dc.title.alternativeMoore's axiom 5₁en_US
dc.typeThesisen_US
dc.type.genreThesisen_US
thesis.degree.departmentMathematicsen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Texas at Austinen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US

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