Some aspects of the theory of barreled spaces
Pedro Pérez Carreras (1987)
Časopis pro pěstování matematiky
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Pedro Pérez Carreras (1987)
Časopis pro pěstování matematiky
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Zdeněk Frolík (1970)
Czechoslovak Mathematical Journal
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B. Cascales, G. Manjabacas, G. Vera (1998)
Studia Mathematica
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Let K be a compact Hausdorff space, the space of continuous functions on K endowed with the pointwise convergence topology, D ⊂ K a dense subset and the topology in C(K) of pointwise convergence on D. It is proved that when is Lindelöf the -compact subsets of C(K) are fragmented by the supremum norm of C(K). As a consequence we obtain some Namioka type results and apply them to prove that if K is separable and is Lindelöf, then K is metrizable if, and only if, there is a countable...
Jerzy Kąkol (1995)
Commentationes Mathematicae Universitatis Carolinae
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We establish the relationship between regularity of a Hausdorff -space and its properties like (K), M.c.c., sequential completeness, local completeness. We give a sufficient and necessary condition for a Hausdorff -space to be an -space. A factorization theorem for -spaces with property (K) is also obtained.
J. E. Jayne (1974)
Annales de l'institut Fourier
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Several equivalent conditions are given for the existence of real-valued Baire functions of all classes on a type of -analytic spaces, called disjoint analytic spaces, and on all pseudocompact spaces. The sequential stability index for the Banach space of bounded continuous real-valued functions on these spaces is shown to be either , or (the first uncountable ordinal). In contrast, the space of bounded real-valued Baire functions of class 1 is shown to contain closed linear subspaces...