Interval topology of lattice effect algebras
نویسندگان
چکیده
منابع مشابه
Divisible effect algebras and interval effect algebras
It is shown that divisible effect algebras are in one-to-one correspondence with unit intervals in partially ordered rational vector spaces.
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Nearly every orthostructure that ha革 been propos磁盘s a model for a logic of 尹ropositions a伍li在ted with a phys沁al 巧slem can be represented as an interval effi苦ct algebra; t如at is, as the p革rtial algeb稳稳nder addition of an ìnt在rval from zero 10 an order unìt i挂在苦硝ially order时 Ab母lian gro辑p. If the sySlem ìs in a state that precludes ce戎ain elements of such an interval, an appropria毛e quotienl ìnle...
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Let L be a lattice ordered effect algebra. We prove that the lattice uniformities on L which make uniformly continuous the operations ⊖ and ⊕ of L are uniquely determined by their system of neighbourhoods of 0 and form a distributive lattice. Moreover we prove that every such uniformity is generated by a family of weakly subadditive [0,+∞]-valued functions on L.
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In this paper we prove the following conclusions: (1). If E is a complete atomic lattice effect algebra, then E is (o)-continuous ⇔ E is order-topological ⇔ E is a totally order-disconnected ⇔ E is algebraic. (2). If E is a complete atomic distributive lattice effect algebra, then its Frink ideal topology τid is Hausdorff topology and is finer than its order topology τo, and τid = τo ⇔ 1 is fin...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2009
ISSN: 0893-9659
DOI: 10.1016/j.aml.2009.01.008