Document Type : Research Paper


1 University of Applied Sciences Stralsund, D-18435 Stralsund, Germany

2 Hebei University of Science and Technology, 050054 Shijiazhuang, P.R.China


We introduce a quantale-valued generalization of approach spaces in terms of quantale-valued gauges. The resulting category is shown to be topological and to possess an initially dense object. Moreover we show that the category of quantale-valued approach spaces defined recently in terms of quantale-valued closures is a coreflective subcategory of our category and, for certain choices of the quantale, is even isomorphic to our category. Finally, the category of quantale-valued metric spaces is shown to be coreflectively embedded in our category.


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