13 citations · 26 across the 7 of their papers we have counts for
8 papers
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…
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…
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…
Tangency vis-a'-vis differentiability by Peano, Severi and Guareschi
Szymon Dolecki, Gabriele H. Greco
Peano defined 'differentiability' of functions and 'lower tangent cones' in 1887, and 'upper tangent cones' in 1903, but uses the latter concept already in 1887 without giving a fo…
Towards historical roots of necessary conditions of optimality. Regula of Peano
Szymon Dolecki, Gabriele H. Greco
At the end of 19th century Peano discerned vector spaces, differentiability, convex sets, limits of families of sets, tangent cones, and many other concepts, in a modern perfect fo…
Group topologies coarser than the Isbell topology
S. Dolecki, F. Jordan, F. Mynard
The Isbell, compact-open and point-open topologies on the set of continuous real-valued maps can be represented as the dual topologies with respect to some collec…