广义度量空间和偏序集

广义度量空间和偏序集都具有函数空间．而函数空间的存在为数学构造和计算提供了很大方便．本文还讨论了广义度量空间和偏序集之间的相互转化问题．

Generalized Metric Spaces and Posets

Generalized metric spaces and posets are both having function spaces. The existence of function spaces of certain mathematical structure facilitates simplification of its constructions and calculations, and requires its category to be closed. The relation between generalized metric spaces and posets is treated. An inclusion order preserving map makes every poset becomes generalized metric space, and induces a functor from a category P of posets to a category M of generalized metric spaces.