Observability for the one-dimensional heat equation
Adherence of minimizers for dual convergences
Flexible niveloids
Towards historical roots of necessary conditions of optimality: Regula of Peano
Topologically maximal pretopologies
Relatively maximal convergences
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 -massimali in una classe superiormente chiusa , cioè massimali fra le -convergenze aventi la stessa imagine per la proiezione su , svolgono un ruolo importante nella teoria dei quozienti; infatti, una mappa -quoziente sulla convergenza -massimale in è automaticamente...
Two-fold theorem on Fréchetness of products
A refined common generalization of known theorems (Arhangel’skii, Michael, Popov and Rančin) on the Fréchetness of products is proved. A new characterization, in terms of products, of strongly Fréchet topologies is provided.
Topologically maximal convergences, accessibility, and covering maps
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...
Inequalities involving -functionals and semi complete lattice homomorphisms
Incomprehensible oblivion on the Peano's legacy
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
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 , the class of -radial topologies contains each sequential topology, then it includes the class of subsequential topologies....
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