Pseudocompactness and the cozero part of a frame
Banaschewski, Bernhard ; Gilmour, Christopher
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996), p. 577-587 / Harvested from Czech Digital Mathematics Library

A characterization of the cozero elements of a frame, without reference to the reals, is given and is used to obtain a characterization of pseudocompactness also independent of the reals. Applications are made to the congruence frame of a $\sigma$-frame and to Alexandroff spaces.

Publié le : 1996-01-01
Classification:  06B10,  54C50,  54D20
@article{118864,
     author = {Bernhard Banaschewski and Christopher Gilmour},
     title = {Pseudocompactness and the cozero part of a frame},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {37},
     year = {1996},
     pages = {577-587},
     zbl = {0881.54018},
     mrnumber = {1426922},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118864}
}
Banaschewski, Bernhard; Gilmour, Christopher. Pseudocompactness and the cozero part of a frame. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) pp. 577-587. http://gdmltest.u-ga.fr/item/118864/

Baboolal D.; Banaschewski B. Compactification and local connectedness of frames, J. Pure Appl. Algebra 70 (1991), 3-16. (1991) | MR 1100502 | Zbl 0722.54031

Banaschewski B. The frame envelope of a $\sigma$-frame, Quaestiones Math. 16.1 (1993), 51-60. (1993) | MR 1217474 | Zbl 0779.06009

Banaschewski B.; Frith J.; Gilmour C. On the congruence lattice of a frame, Pacific J. Math. 130.2 (1987), 209-213. (1987) | MR 0914098 | Zbl 0637.06006

Banaschewski B.; Gilmour C. Stone-Čech compactification and dimension theory for regular $\sigma$-frames, J. London Math. Soc. (2) No.127, 39, part 1 (1989), 1-8. | MR 0989914 | Zbl 0675.06005

Banaschewski B.; Mulvey C. Stone-Čech compactification of locales I, Houston J. of Math. 6.3 (1980), 301-312. (1980) | MR 0597771 | Zbl 0473.54026

Banaschewski B.; Mulvey C. Stone-Čech compactification of locales II, J. Pure Appl. Algebra 33 (1984), 107-122. (1984) | MR 0754950 | Zbl 0549.54017

Banaschewski B.; Pultr A. Paracompactness revisited, Applied Categorical Structures 1 (1993), 181-190. (1993) | MR 1245799 | Zbl 0797.54032

Gilmour C. Realcompact Alexandroff spaces and regular $\sigma$-frames, PhD Thesis, University of Cape Town, 1981. | Zbl 0601.54019

Gilmour C. Realcompact Alexandroff spaces and regular $\sigma$-frames, Math. Proc. Cambridge Philos. Soc. 96 (1984), 73-79. (1984) | MR 0743702

Gordon H. Rings of functions determined by zero-sets, Pacific J. Math. 36 (1971), 133-157. (1971) | MR 0320996 | Zbl 0185.38803

Johnstone P.T. Stone Spaces, Cambridge Studies in Advanced Math. 3, Cambridge Univ. Press, 1982. | MR 0698074 | Zbl 0586.54001

Kennison J. $m$-Pseudocompactness, Trans. Amer. Math. Soc. 104 (1962), 436-442. (1962) | MR 0145478 | Zbl 0111.35004

Madden J. $\kappa$-Frames, J. Pure Appl. Algebra 70 (1991), 107-127. (1991) | MR 1100510 | Zbl 0721.06006

Madden J.; Vermeer H. Lindelöf locales and realcompactness, Math. Proc. Camb. Phil. Soc. 99 (1986), 473-480. (1986) | MR 0830360 | Zbl 0603.54021

Marcus N. Realcompactifications of frames, MSc Thesis, University of Cape Town, 1994.

Reynolds G. On the spectrum of a real representable ring, Applications of Sheaves, Springer LNM 753 (1977), 595-611. | MR 0555563 | Zbl 0426.18002

Reynolds G. Alexandroff algebras and complete regularity, Proc. Amer. Math. Soc. 76 (1979), 322-326. (1979) | MR 0537098 | Zbl 0416.54015

Walters J. Uniform sigma frames and the cozero part of uniform frames, MSc Thesis, University of Cape Town, 1990.

Walters J. Compactifications and uniformities on sigma frames, Comment. Math. Univ. Carolinae 32.1 (1991), 189-198. (1991) | MR 1118301 | Zbl 0735.54014