منابع مشابه
On compactness of lattices
In this paper, we present a study of various concepts pertaining to compactness properties of a lattice. Special cases include such notions as countably compactness, almost countably compactness, and countably paracompactness. Some investigations in these matters have been done in [2, 7, 14]. We go beyond these results and introduce new subsets of I(L) and their lattices to investigate. This wa...
متن کاملWeak Limits of Projections and Compactness of Subspace Lattices
A strongly closed lattice of projections on a Hubert space is compact if the associated algebra of operators has a weakly dense subset of compact operators. If the lattice is commutative, there are necessary and sufficient conditions for compactness, one in terms of the structure of the lattice, and the other in terms of a measure on the lattice. There are many examples of compact lattices, and...
متن کاملSimple axiomatization of reticulations on residuated lattices
We give a simple and independent axiomatization of reticulations on residuated lattices, which were axiomatized by five conditions in [C. Mureşan, The reticulation of a residuated lattice, Bull. Math. Soc. Sci. Math. Roumanie 51 (2008), no. 1, 47--65]. Moreover, we show that reticulations can be considered as lattice homomorphisms between residuated lattices and b...
متن کاملOn Compactness Theorem
In this talk we investigate the compactness theorem (as a property) in non-classical logics. We focus on the following problems: (a) What kind of semantics make a logic having compactnesss theorem? (b) What is the relationship between the compactness theorem and the classical model existence theorem (CME)/model existence theorem?
متن کاملOn the Characterizations of Compactness
In the paper we show equivalence of the convergence of filters on a topological space and the convergence of nets in the space. We also give, five characterizations of compactness. Namely, for any topological space T we proved that following condition are equivalent: • T is compact, • every ultrafilter on T is convergent, • every proper filter on T has cluster point, • every net in T has cluste...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2005
ISSN: 0161-1712,1687-0425
DOI: 10.1155/ijmms.2005.2565