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Title: Perfect compactifications of frames (English)
Author: Baboolal, Dharmanand
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 61
Issue: 3
Year: 2011
Pages: 845-861
Summary lang: English
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Category: math
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Summary: Perfect compactifications of frames are introduced. It is shown that the Stone-Čech compactification is an example of such a compactification. We also introduce rim-compact frames and for such frames we define its Freudenthal compactification, another example of a perfect compactification. The remainder of a rim-compact frame in its Freudenthal compactification is shown to be zero-dimensional. It is shown that with the assumption of the Boolean Ultrafilter Theorem the Freudenthal compactification for spaces, as well as the Freudenthal-Morita Theorem for spaces, can be obtained from our frame constructions. (English)
Keyword: perfect compactifications
Keyword: rim-compact frame
MSC: 06B35
MSC: 06D20
MSC: 54D35
idZBL: Zbl 1249.06027
idMR: MR2853096
DOI: 10.1007/s10587-011-0032-z
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Date available: 2011-09-22T14:51:54Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/141643
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Reference: [9] Morita, K.: On bicompactifications of semibicompact spaces.Sci. Rep. Tokyo Bunrika Daigaku, Sect. A. 4 (1952), 222-229. Zbl 0049.39801, MR 0052089
Reference: [10] Schechter, E.: Handbook of Analysis and its Foundations.Academic Press San Diego (1997). Zbl 0943.26001, MR 1417259
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Reference: [12] Thron, W. J.: Topological Structures.Holt, Rinehart and Winston New York-Chicago-San Francisco-Toronto-London (1966). Zbl 0137.15402, MR 0200892
Reference: [13] Willard, S.: General Topology.Addison-Wesley Reading (1970). Zbl 0205.26601, MR 0264581
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