The Meet-continuity of L-semilattices

摘要

This paper is devoted to search for Cartesian closed category of quantitative domain categories. Firstly, inspired by the method of constructing L -frames, the meet-continuity on L -semilattices is built and characterized, which generalizes the meet-continuity on crisp semilattices. Then, it is shown that a complete L -lattice is an L -frame iff it is distributive and meet-continuous. In particular, it is shown that the category L - MC of meet-continuous L -lattices is cartesian closed.