A note on the category of quasi-proximity spaces. (English) Zbl 1474.54056
Summary: We characterize the separation properties \(T_0\) and \(T_1\) at a point \(p\) in the category of quasi-proximity spaces. Moreover, the (strongly) closed and (strongly) open subobjects of an object, and each of the various notions of connected and compact objects are characterized in this topological category.
MSC:
| 54B30 | Categorical methods in general topology |
| 54D10 | Lower separation axioms (\(T_0\)–\(T_3\), etc.) |
| 54A05 | Topological spaces and generalizations (closure spaces, etc.) |
| 54E05 | Proximity structures and generalizations |
| 18B99 | Special categories |
Keywords:
topological category; quasi-proximity space; separation; closedness; connectedness; compactnessReferences:
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