2006•Mohu xitong yu shuxueRequires access

Some Theorems on the Weights of Continuous Posets and Smyth Power Domains

Hai Liu

Abstract

The concept of weights on continuous domains is generalised to the setting of continuous(posets.) Relations of the weights of a continuous poset,the directed completion of the poset and some intrinsic topologyies on the poset are examined.The main theorems are:(1) The weight of a(continuous) poset is equal to the weight of the Scott topology and is also equal to the weight of the(Lawson) topology(of the poset).(2) The weight of a continuous poset is equal to the weight of the(directed) completion of the poset.(3) The weight of an infinite continuous domain is equal to the(weight) of its Smyth power domain.(4) The weight of a finite domain is less than or equal to that of its Smyth power domain.

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Key concepts: Partially ordered set, Mathematics, Domain (mathematical analysis), Domain theory, Power domains, Combinatorics, Discrete mathematics, Power (physics)