Spaces modelled by an algebra on [0, infinity] and their complete objects

作者：Colebunders E^*; Giuli E; Lowen R

来源：Topology and Its Applications, 2010, 157(8): 1335-1346.

DOI：10.1016/j.topol.2009.05.016

• Affine object
• Zariski closure
• Separated object
• Complete object
• Approach space
• (Quasi) metric space
• Topological space
• Non-Archimedean space

We study constructs of type [0, infinity]Set(Omega) consisting of affine sets over [0, infinity] modelled by some algebra Omega The categorical theory of closure operators is used to study separated and complete objects with respect to the Zariski closure operator, naturally defined in any category [0, infinity]Set(Omega) Several basic examples are provided, in particular we show that the construct of approach spaces. the constructs of pseudo (quasi) metric spaces with contractions.

• 出版日期2010-6-1