Sublocale sets and sublocale lattices
Archivum mathematicum, Tome 42 (2006) no. 4, pp. 409-418
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We present very short and simple proofs of such facts as co-frame distributivity of sublocales, zero-dimensionality of the resulting co-frames, Isbell’s Density Theorem and characteristic properties of fit and subfit frames, using sublocale sets.
We present very short and simple proofs of such facts as co-frame distributivity of sublocales, zero-dimensionality of the resulting co-frames, Isbell’s Density Theorem and characteristic properties of fit and subfit frames, using sublocale sets.
Classification : 06D22
Keywords: frames; sublocales; coframe of sublocales; fitness and subfitness
@article{ARM_2006_42_4_a5,
     author = {Picado, Jorge and Pultr, Ale\v{s}},
     title = {Sublocale sets and sublocale lattices},
     journal = {Archivum mathematicum},
     pages = {409--418},
     year = {2006},
     volume = {42},
     number = {4},
     mrnumber = {2283021},
     zbl = {1164.06313},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2006_42_4_a5/}
}
TY  - JOUR
AU  - Picado, Jorge
AU  - Pultr, Aleš
TI  - Sublocale sets and sublocale lattices
JO  - Archivum mathematicum
PY  - 2006
SP  - 409
EP  - 418
VL  - 42
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ARM_2006_42_4_a5/
LA  - en
ID  - ARM_2006_42_4_a5
ER  - 
%0 Journal Article
%A Picado, Jorge
%A Pultr, Aleš
%T Sublocale sets and sublocale lattices
%J Archivum mathematicum
%D 2006
%P 409-418
%V 42
%N 4
%U http://geodesic.mathdoc.fr/item/ARM_2006_42_4_a5/
%G en
%F ARM_2006_42_4_a5
Picado, Jorge; Pultr, Aleš. Sublocale sets and sublocale lattices. Archivum mathematicum, Tome 42 (2006) no. 4, pp. 409-418. http://geodesic.mathdoc.fr/item/ARM_2006_42_4_a5/

[1] Davey B. A., Priestley H. A.: Introduction to Lattices and Order. Second Edition, Cambridge University Press, 2001. | MR | Zbl

[2] Isbell J. R.: Atomless parts of spaces. Math. Scand. 31 (1972), 5–32. | MR | Zbl

[3] Johnstone P. T.: Stone Spaces. Cambridge Stud. Adv. Math. No 3, Cambridge University Press, 1983. | MR

[4] Mac Lane S.: Categories for the Working Mathematician. Springer-Verlag, New York, 1971. | MR | Zbl

[5] Picado J., Pultr A., Tozzi A.: Locales. In: M. C. Pedicchio and W. Tholen (Eds.), Categorical Foundations - Special Topics in Order, Topology, Algebra and Sheaf Theory, Encyclopedia of Mathematics and its Applications, Vol. 97, Cambridge University Press, 2003, pp. 49–101. | MR | Zbl

[6] Priestley H. A.: Representation of distributive lattices by means of ordered Stone spaces. Bull. London Math. Soc. 2 (1970), 186–190. | MR | Zbl

[7] Priestley H. A.: Ordered topological spaces and the representation of distributive lattices. Proc. London Math. Soc. 324 (1972), 507–530. | MR | Zbl

[8] Pultr A., Sichler J.: Frames in Priestley duality. Cahiers Topologie Géom. Différentielle Catég. XXIX (1988), 193–202. | MR

[9] Pultr A., Sichler J.: A Priestley view of spatialization of frames. Cahiers Topologie Géom. Différentielle Catég. XLI (2000), 225–238. | MR | Zbl

[10] Simmons H.: The lattice theoretic part of topological separation properties. Proc. Edinburgh Math. Soc. (2) 21 (1978), 41–48. | MR | Zbl