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Relatively maximal convergences

Szymon DoleckiMichel Pillot — 1998

Bollettino dell'Unione Matematica Italiana

Topologie, pretopologie, paratopologie e pseudotopologie sono importanti classi di convergenze, chiuse per estremi superiori (superiormente chiuse) ed inoltre caratterizzabili mediante le aderenze di certi filtri. Convergenze J -massimali in una classe superiormente chiusa D J , cioè massimali fra le D -convergenze aventi la stessa imagine per la proiezione su J , svolgono un ruolo importante nella teoria dei quozienti; infatti, una mappa J -quoziente sulla convergenza J -massimale in D è automaticamente...

Topologically maximal convergences, accessibility, and covering maps

Szymon DoleckiMichel Pillot — 1998

Mathematica Bohemica

Topologically maximal pretopologies, paratopologies and pseudotopologies are characterized in terms of various accessibility properties. Thanks to recent convergence-theoretic descriptions of miscellaneous quotient maps (in terms of topological, pretopological, paratopological and pseudotopological projections), the quotient characterizations of accessibility (in particular, those of G. T. Whyburn and F. Siwiec) are shown to be instances of a single general theorem. Convergence-theoretic characterizations...

Incomprehensible oblivion on the Peano's legacy

Szymon DoleckiGabriele H. Greco — 2012

Antiquitates Mathematicae

Giuseppe Peano (27.10.1858-20.04.1932) made ​​many discoveries and introduced many concepts that are attributed to other mathematicians, even though their contribution was late and often less significant. Our main goal is to guide those of his achievements, which are the least known and an indication of the value of others that seem to be under-appreciated. We will also on the causes of the incomprehensible oblivion. Peano began studying mathematics at the University of Turin in 1876, and graduated...

Extension of multisequences and countably uniradial classes of topologies

Szymon DoleckiAndrzej StarosolskiStephen W. Watson — 2003

Commentationes Mathematicae Universitatis Carolinae

It is proved that every non trivial continuous map between the sets of extremal elements of monotone sequential cascades can be continuously extended to some subcascades. This implies a result of Franklin and Rajagopalan that an Arens space cannot be continuously non trivially mapped to an Arens space of higher rank. As an application, it is proved that if for a filter on ω , the class of -radial topologies contains each sequential topology, then it includes the class of subsequential topologies....

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