几种格上拓扑空间范畴中乘积与上积运算的封闭性

Closeness of Product and Coprodnct Operation in Several Kinds ofthe Category of Lattice-valued Topofogical Spaces

本文引入四种格上拓扑空间范畴，分别讨论了其中的乘积与上积运算，以及相应的结构性、唯一性和存在性问题。通过讨论，给出了一种比较理想的格上拓扑空间的乘积空间，并指出目前使用的格上拓扑空间的乘积空间具有一定的局限性，其所属范畴的态射是Ｚａｄｅｈ型映射，这类映射保持Ｆｕｚｚｙ点的高度不变，隐含度量不变性。

This paper introduces four kinds of the category of lattice-valued topologicalspaces, and discusses the product and the coproduct operation among it respectively,and the problems of its relevant structureness, uniqueness and existenceness. Throughdiscussion, this paper gives more satisfactory product space of lattice-valued topologicalspaces, points out that commonly-used the product space of lattice-valued topologicalspaces at present has definite limitation, and morphism of the category is Zadeh's typemapping, these type of mapping keeps the height of fuzzy point unchangeable, andimplys metric unchangeable.