Compactifications and uniformities on sigma frames

Joanne L. Walters-Wayland

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 1, page 189-198
  • ISSN: 0010-2628

Abstract

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A bijective correspondence between strong inclusions and compactifications in the setting of σ -frames is presented. The category of uniform σ -frames is defined and a description of the Samuel compactification is given. It is shown that the Samuel compactification of a uniform frame is completely determined by the σ -frame consisting of its uniform cozero part, and consequently, any compactification of any frame is so determined.

How to cite

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Walters-Wayland, Joanne L.. "Compactifications and uniformities on sigma frames." Commentationes Mathematicae Universitatis Carolinae 32.1 (1991): 189-198. <http://eudml.org/doc/247245>.

@article{Walters1991,
abstract = {A bijective correspondence between strong inclusions and compactifications in the setting of $\sigma $-frames is presented. The category of uniform $\sigma $-frames is defined and a description of the Samuel compactification is given. It is shown that the Samuel compactification of a uniform frame is completely determined by the $\sigma $-frame consisting of its uniform cozero part, and consequently, any compactification of any frame is so determined.},
author = {Walters-Wayland, Joanne L.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {strong inclusion; compactification; uniform $\sigma $-frame; uniform cozero; sigma frames; Samuel compactification},
language = {eng},
number = {1},
pages = {189-198},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Compactifications and uniformities on sigma frames},
url = {http://eudml.org/doc/247245},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Walters-Wayland, Joanne L.
TI - Compactifications and uniformities on sigma frames
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 1
SP - 189
EP - 198
AB - A bijective correspondence between strong inclusions and compactifications in the setting of $\sigma $-frames is presented. The category of uniform $\sigma $-frames is defined and a description of the Samuel compactification is given. It is shown that the Samuel compactification of a uniform frame is completely determined by the $\sigma $-frame consisting of its uniform cozero part, and consequently, any compactification of any frame is so determined.
LA - eng
KW - strong inclusion; compactification; uniform $\sigma $-frame; uniform cozero; sigma frames; Samuel compactification
UR - http://eudml.org/doc/247245
ER -

References

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  1. Banaschewski B., Frames and compactifications, Proc. I. International Symp. on Extension Theory of Topological Structures and Its Applications. VEB Deutscher Verlag der Wissenschaften, 1969. Zbl0188.28006
  2. Banaschewski B., Gilmour C.R.A., Stone-Čech compactification and dimension theory for regular σ -frames, J. London Math. Soc.(2) No. 127, 39, part 1 1-8 (1989). (1989) Zbl0675.06005MR0989914
  3. Banaschewski B., Mulvey C., Stone-Čech compactification of Locales I., Houston J. of Math. 6, 3 (1980), 301-312. (1980) Zbl0473.54026MR0597771
  4. Frith J.L., The Category of Uniform Frames, Cahier de Topologie et Geometrie, to appear. Zbl0738.18002MR1109372
  5. Gilmour C.R.A., Realcompact Alexandroff spaces and regular σ -frames, Math. Proc. Cambridge Philos. Soc. 96 (1984), 73-79. (1984) MR0743702
  6. Ginsburg S., Isbell J.R., Some operators on uniform spaces, Trans. Amer. Math. Soc. 36 (1959), 145-168. (1959) Zbl0087.37601MR0112119
  7. Johnstone P.T., Stone Spaces, Cambridge Studies in Advanced Math. 3, Cambridge Univ. Press, 1982. Zbl0586.54001MR0698074
  8. Madden J., Vermeer H., Lindelöf locales and realcompactness, Math. Proc. Camb. Phil. Soc. (1985), 1-8. (1985) 
  9. Pultr A., Pointless uniformities I. Complete regularity, Comment. Math. Univ. Carolinae 25 (1984), 91-104. (1984) Zbl0543.54023MR0749118

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