Samuel compactification and uniform coreflection of nearness σ -frames

Inderasan Naidoo

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 4, page 1229-1241
  • ISSN: 0011-4642

Abstract

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We introduce the structure of a nearness on a σ -frame and construct the coreflection of the category 𝐍 σ F r m of nearness σ -frames to the category 𝐊 R e g σ F r m of compact regular σ -frames. This description of the Samuel compactification of a nearness σ -frame is in analogy to the construction by Baboolal and Ori for nearness frames in [1] and that of Walters for uniform σ -frames in [11]. We also construct the uniform coreflection of a nearness σ -frame, that is, the coreflection of the category of 𝐍 σ F r m to the category U σ Frm of uniform σ -frames.

How to cite

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Naidoo, Inderasan. "Samuel compactification and uniform coreflection of nearness $\sigma $-frames." Czechoslovak Mathematical Journal 56.4 (2006): 1229-1241. <http://eudml.org/doc/31102>.

@article{Naidoo2006,
abstract = {We introduce the structure of a nearness on a $\sigma $-frame and construct the coreflection of the category $\{\mathbf \{N\}\sigma Frm\}$ of nearness $\sigma $-frames to the category $\{\mathbf \{K\}Reg\sigma Frm\}$ of compact regular $\sigma $-frames. This description of the Samuel compactification of a nearness $\sigma $-frame is in analogy to the construction by Baboolal and Ori for nearness frames in [1] and that of Walters for uniform $\sigma $-frames in [11]. We also construct the uniform coreflection of a nearness $\sigma $-frame, that is, the coreflection of the category of $\{\mathbf \{N\}\sigma Frm\}$ to the category U$\sigma $Frm of uniform $\sigma $-frames.},
author = {Naidoo, Inderasan},
journal = {Czechoslovak Mathematical Journal},
keywords = {$\sigma $-frame; nearness; Samuel compactification; -frame; nearness; Samuel compactification},
language = {eng},
number = {4},
pages = {1229-1241},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Samuel compactification and uniform coreflection of nearness $\sigma $-frames},
url = {http://eudml.org/doc/31102},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Naidoo, Inderasan
TI - Samuel compactification and uniform coreflection of nearness $\sigma $-frames
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 4
SP - 1229
EP - 1241
AB - We introduce the structure of a nearness on a $\sigma $-frame and construct the coreflection of the category ${\mathbf {N}\sigma Frm}$ of nearness $\sigma $-frames to the category ${\mathbf {K}Reg\sigma Frm}$ of compact regular $\sigma $-frames. This description of the Samuel compactification of a nearness $\sigma $-frame is in analogy to the construction by Baboolal and Ori for nearness frames in [1] and that of Walters for uniform $\sigma $-frames in [11]. We also construct the uniform coreflection of a nearness $\sigma $-frame, that is, the coreflection of the category of ${\mathbf {N}\sigma Frm}$ to the category U$\sigma $Frm of uniform $\sigma $-frames.
LA - eng
KW - $\sigma $-frame; nearness; Samuel compactification; -frame; nearness; Samuel compactification
UR - http://eudml.org/doc/31102
ER -

References

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  8. Stone Spaces. Cambridge Studies in Advanced Math. No.  3, Cambridge University Press, Cambridge, 1982. (1982) MR0698074
  9. κ -frames, J.  Pure Appl. Algebra 70 (1991), 107–127. (1991) Zbl0721.06006MR1100510
  10. Nearness and convergence in pointfree topology, PhD.  Thesis, University of Cape Town, Cape Town, 2004. (2004) 
  11. Uniform sigma frames and the cozero part of uniform frames, Masters Dissertation, University of Cape Town, Cape Town, 1990. (1990) 
  12. Compactifications and uniformities on σ -frames, Comm. Math. Univ. Carolinae 32 (1991), 189–198. (1991) Zbl0735.54014MR1118301
  13. Completeness and nearly fine uniform frames, PhD.  Thesis, Univ. Catholique de Louvain, Louvain, 1996. (1996) 

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