Perfect compactifications of frames

Dharmanand Baboolal

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 3, page 845-861
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Baboolal, Dharmanand. "Perfect compactifications of frames." Czechoslovak Mathematical Journal 61.3 (2011): 845-861. <http://eudml.org/doc/196919>.

@article{Baboolal2011,
abstract = {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.},
author = {Baboolal, Dharmanand},
journal = {Czechoslovak Mathematical Journal},
keywords = {perfect compactifications; rim-compact frame; perfect compactification; rim-compact frame},
language = {eng},
number = {3},
pages = {845-861},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Perfect compactifications of frames},
url = {http://eudml.org/doc/196919},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Baboolal, Dharmanand
TI - Perfect compactifications of frames
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 3
SP - 845
EP - 861
AB - 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.
LA - eng
KW - perfect compactifications; rim-compact frame; perfect compactification; rim-compact frame
UR - http://eudml.org/doc/196919
ER -

References

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  9. Morita, K., On bicompactifications of semibicompact spaces, Sci. Rep. Tokyo Bunrika Daigaku, Sect. A. 4 (1952), 222-229. (1952) Zbl0049.39801MR0052089
  10. Schechter, E., Handbook of Analysis and its Foundations, Academic Press San Diego (1997). (1997) Zbl0943.26001MR1417259
  11. Sklyarenko, E. G., 10.1090/trans2/058/11, Am. Math. Soc. Transl. 58 (1966), 216-244. (1966) DOI10.1090/trans2/058/11
  12. Thron, W. J., Topological Structures, Holt, Rinehart and Winston New York-Chicago-San Francisco-Toronto-London (1966). (1966) Zbl0137.15402MR0200892
  13. Willard, S., General Topology, Addison-Wesley Reading (1970). (1970) Zbl0205.26601MR0264581

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