3 papers
math.GN2020
Acquiring a dimension: from topology to convergence theory
Szymon Dolecki
Convergence theory is an extension of general topology. In contrast with topology, it is closed under some important operations, like exponentiation. With all its advantages, conve…
math.GN2020
Multiple facets of inverse continuity
Szymon Dolecki
Inversion of various inclusions, that characterize continuity in topological spaces, results in numerous variants of quotient and perfect maps. In the framework of convergences, th…
math.GN2019
Continuous extension of maps between sequential cascades
Szymon Dolecki, Andrzej Starosolski
The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour opera…