Gunther Jager - University of Applied Sciences Stralsund, D-۱۸۴۳۵ Stralsund, Germany
Wei Yao - Hebei University of Science and Technology, ۰۵۰۰۵۴ 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.

L-gauge space, L-approach space, L-metric space, Continuity space