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UBC Theses and Dissertations
The structure of βN Rambally, Rodney Seunarine
Abstract
Our subject matter consists of a survey of the major results concerning the topological space βN-N where N represents the space of natural numbers with the discrete topology, and βN the Stone-Čech compactification of N . We are mainly concerned with the results which were derived during the last ten years. When there is no advantage in restricting our work to the space N we work with an arbitrary discrete space X and finally formulate our results in terms of βN-N . In some cases, pre-1960 results concerning βN-N are obtained as special cases of the results we derive using an arbitrary discrete space X . The material presented is divided into four chapters. In Chapter I, we discuss certain subsets of βN-N which can be C*-embedded in other subsets of βN-N . This study leads to the conclusion that no proper dense subset of βN-N can be C*-embedded. In the second chapter we devise a general method of associating certain classes of points of βN-N with certain subalgebras of C(N) . The P-points of βN-N form one of these classes. The answer to R. S. Pierce's question, "Does there exist a point of βN-N which lies simultaneously in the closures of three pairwise disjoint open sets" is discussed in Chapter III. Finally in Chapter IV we present two proofs of the non-homogeneity of βN-N , without the use of the Continuum Hypothesis.
Item Metadata
Title |
The structure of βN
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1970
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Description |
Our subject matter consists of a survey of the major results concerning the topological space βN-N where N represents the space of natural numbers with the discrete topology, and βN the Stone-Čech compactification of N . We are mainly concerned with the results which were derived during the last ten years.
When there is no advantage in restricting our work to the space N we work with an arbitrary discrete space X and finally formulate our results in terms of βN-N . In some cases, pre-1960 results concerning βN-N are obtained as special cases of the results we derive using an arbitrary discrete space X . The material presented is divided into four chapters.
In Chapter I, we discuss certain subsets of βN-N which can be C*-embedded in other subsets of βN-N . This study leads to the conclusion that no proper dense subset of βN-N can be C*-embedded. In the second chapter we devise a general method of associating certain classes of points of βN-N with certain subalgebras of C(N) . The P-points of βN-N form one of these classes. The answer to R. S. Pierce's question, "Does there exist a point of βN-N which lies simultaneously
in the closures of three pairwise disjoint open sets" is discussed in Chapter III. Finally in Chapter IV we present two proofs of the non-homogeneity of βN-N , without the use of the Continuum Hypothesis.
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Genre | |
Type | |
Language |
eng
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Date Available |
2011-06-14
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0080516
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URI | |
Degree | |
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Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.