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The 17th topological type of [omega-star]

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Jonathan Verner (Creator)
Institution
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/
Advisor
Jerry Vaughan

Abstract: "It has long been known, that omega-star is not homogeneous. In fact, it was proved by Frolik that the Čech-Stone growth of any non-pseudocompact space X is not homogeneous. Frolik's result, which was non-constructive" in nature, prompted interest in finding specific, topological reasons for the nonhomogeneity of the Čech-Stone growths of non-pseudocompact spaces in general and omega-star in particular. To this day, there have been discovered a total of 16 topological types in omega-star, such as Kunen's weak P-points. We investigate along these lines, defining another topological type called a uniquely omega-accessible point. Such a point is known to exist in omega-star under MA and in this work we investigate a method possibly leading to a proof in ZFC. The main result of this thesis is the construction of two irresolvable spaces one with a remote point and the other with a weak P-point. "--Abstract from author supplied metadata.

Additional Information

Publication
Thesis
Language: English
Date: 2006
Keywords
omega-star, Frolik, non-pseudocompact space X, nonhomogeneity
Subjects
Topological spaces
Topology spaces
Critical point theory (Mathematical analysis)