# Compactifications and uniformities on sigma frames

Commentationes Mathematicae Universitatis Carolinae (1991)

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

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topWalters-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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- Frith J.L., The Category of Uniform Frames, Cahier de Topologie et Geometrie, to appear. Zbl0738.18002MR1109372
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- Ginsburg S., Isbell J.R., Some operators on uniform spaces, Trans. Amer. Math. Soc. 36 (1959), 145-168. (1959) Zbl0087.37601MR0112119
- Johnstone P.T., Stone Spaces, Cambridge Studies in Advanced Math. 3, Cambridge Univ. Press, 1982. Zbl0586.54001MR0698074
- Madden J., Vermeer H., Lindelöf locales and realcompactness, Math. Proc. Camb. Phil. Soc. (1985), 1-8. (1985)
- Pultr A., Pointless uniformities I. Complete regularity, Comment. Math. Univ. Carolinae 25 (1984), 91-104. (1984) Zbl0543.54023MR0749118

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