Categorical Topology pp 69-79 | Cite as
On the Largest Coreflective Cartesian Closed Subconstruct of Prtop
Chapter
Abstract
We show that the subconstruct Fing of Prtop, consisting of all finitely generated pre-topological spaces, is the largest Cartesian closed coreflective subconstruct of Prtop. This implies that in any coreflective subconstruct of Prtop, exponential objects are finitely generated. Moreover, in any finitely productive, coreflective subconstruct, exponential objects are precisely those objects of the subconstruct that are finitely generated. We give a counterexample showing that without finite productivity the previous result does not hold.
Key words
pretopological space finitely generated space exponential object quasi-variety Cartesian closednessMathematics Subject Classifications (1991)
54B30 18D15 54A05Preview
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