Geodesic
Perfect compactifications of frames
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 3, pp. 845-861
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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.
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.
DOI : 10.1007/s10587-011-0032-z
Classification : 06B35, 06D20, 54D35
Keywords: perfect compactifications; rim-compact frame 
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Baboolal, Dharmanand. Perfect compactifications of frames. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 3, pp. 845-861. doi: 10.1007/s10587-011-0032-z

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