It is known that if a topological space X is locally compact then the Kuratowski convergence on the closed subsets of X is topological. We show that the converse is true, provided that X is quasi-sober. We also show that the Kuratowski convergence is topological if and only if it is pretopological.
When is Kuratowski convergence topological?
VITOLO, Paolo
1998-01-01
Abstract
It is known that if a topological space X is locally compact then the Kuratowski convergence on the closed subsets of X is topological. We show that the converse is true, provided that X is quasi-sober. We also show that the Kuratowski convergence is topological if and only if it is pretopological.File in questo prodotto:
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