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On Alexandrov lattices

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  • Albert Gorelishvili

Abstract

By an Alexandrov lattice we mean a δ normal lattice of subsets of an abstract set X , such that the set of ℒ -regular countably additive bounded measures is sequentially closed in the set of ℒ -regular finitely additive bounded measures on the algebra generated by ℒ with the weak topology. For a pair of lattices ℒ 1 ⊂ ℒ 2 in X sufficient conditions are indicated to determine when ℒ 1 Alexandrov implies that ℒ 2 is also Alexandrov and vice versa. The extension of this situation is given where T : X → Y and ℒ 1 and ℒ 2 are lattices of subsets of X and Y respectively and T is ℒ 1 − ℒ 2 continuous.

Suggested Citation

  • Albert Gorelishvili, 1993. "On Alexandrov lattices," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 16, pages 1-11, January.
    • Handle: RePEc:hin:jijmms:218257
    DOI: 10.1155/S0161171293000055
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