Far Eastern Mathematical Journal

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Categorical topological spaces and dimensions


E. E. Skurikhin

2008, issue 1, P. 96–110


Abstract
A categorical topological space is a generalized object of an arbitrary Grothendieck site with the structure of its subobjects. The concept of categorical topological space was developed in previous works of author. This paper continuous this theme with an emphasis to applications to dimension theory.

Keywords:
Grothendieck topology, sheaves, Grothendieck cohomology, presheaves of sets, dimension

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References

[1] M. Kashivara, P. Shapira, Puchki na mnogoobraziyax, Mir, M., 1997, 656 s.
[2] A. Grothendieck, Seminaire Geometrie Algebriqe 4 [SGA4] (with M. Artin and J.-L. Verdier), Theorie de topos et cogomologie etale de shemas, Lecture Notes in Mathematics, 269, Springer-Verlang, Hedelberg, 1972, 270 pp.
[3] E. E. Skurixin, “Puchkovye kogomologii predpuchkov mnozhestv i nekotorye ix prilozheniya”, Tr. Mat. in-ta im. V. A. Steklova RAN, 193, 1992, 169–173.
[4] E. E. Skurixin, Puchkovye kogomologii i polnye braue'rovy reshetki, Dal'nauka, Vladivostok, 1993, 218 s.
[5] E. E. Skurixin, “Puchkovye kogomologii i razmernost' chastichno uporyadochennyx mnozhestv”, Tr. Mat. in-ta im. V. A. Steklova RAN, 239, 2002, 289–317.
[6] E. E. Skurixin, Puchki na normal'nyx i parakompaktnyx reshetkax, Dal'nauka, Vladivostok, 1998, 145 s.
[7] E. E. Skurixin, Puchkovye kogomologii i razmernost' chastichno uporyadochennyx mnozhestv, Dal'nauka, Vladivostok, 2004, 194 s.
[8] E. E. Skurixin, Vyalye puchki i puchkovye kogomologii ravnomernyx prostranstv, Preprint № 9 In-ta prikl. matem. DVO RAN, Dal'nauka, Vladivostok, 2002, 8 s.
[9] E. E. Skurixin, “Puchkovye kogomologii i razmernost' ravnomernyx prostranstv”, Uspexi mat. nauk, 58:4 (2003), 157–158.
[10] E. E. Skurixin, “Kogomologii i razmernost' kvaziuporyadochennyx mnozhestv”, Uspexi mat. nauk, 56:1 (2001), 179–180.
[11] E. E. Skurixin, “Ob odnom klasse kategornyx topologicheskix prostranstv”, Uspexi mat. nauk, 63:1 (2008), 167–168.
[12] A. G. Suxonos, Kogomologicheskaya xarakteristika dliny chastichno uporyadochennogo mnozhestva, Preprint № 7 In-ta prikl. matem. DVO RAN, Dal'nauka, Vladivostok, 2006, 8 s.
[13] E. E. Skurixin, A. G. Suxonos, “Kogomologii i razmernost' prostranstv Chu”, Dal'nev. matem. Zhurnal, 6:1-2 (2005), 14–22.

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