Displaying similar documents to “A revised closed graph theorem for quasi-Suslin spaces”

Fragmentability and compactness in C(K)-spaces

B. Cascales, G. Manjabacas, G. Vera (1998)

Studia Mathematica

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Let K be a compact Hausdorff space, C p ( K ) the space of continuous functions on K endowed with the pointwise convergence topology, D ⊂ K a dense subset and t p ( D ) the topology in C(K) of pointwise convergence on D. It is proved that when C p ( K ) is Lindelöf the t p ( D ) -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 C p ( K ) is Lindelöf, then K is metrizable if, and only if, there is a countable...

Remarks on bounded sets in ( L F ) t v -spaces

Jerzy Kąkol (1995)

Commentationes Mathematicae Universitatis Carolinae

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We establish the relationship between regularity of a Hausdorff ( L B ) t v -space and its properties like (K), M.c.c., sequential completeness, local completeness. We give a sufficient and necessary condition for a Hausdorff ( L B ) t v -space to be an ( L S ) t v -space. A factorization theorem for ( L N ) t v -spaces with property (K) is also obtained.

Space of Baire functions. I

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 K -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 0 , 1 , or Ω (the first uncountable ordinal). In contrast, the space of bounded real-valued Baire functions of class 1 is shown to contain closed linear subspaces...