Displaying similar documents to “The dual of the space of holomorphic functions on locally closed convex sets.”

On the Toëplitz corona problem.

Eric Amar (2003)

Publicacions Matemàtiques

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The aim of this note is to characterize the vectors g = (g, . . . ,g) of bounded holomorphic functions in the unit ball or in the unit polydisk of C such that the Corona is true for them in terms of the H Corona for measures on the boundary.

A Schwarz lemma for correspondences and applications.

Kaushal Verma (2003)

Publicacions Matemàtiques

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A version of the Schwarz lemma for correspondences is studied. Two applications are obtained namely, the 'non-increasing' property of the Kobayashi metric under correspondences and a weak version of the Wong-Rosay theorem for convex, finite type domains admitting a 'non-compact' family of proper correspondences.

Selections generating new topologies.

Valentin Gutev, Artur Tomita (2007)

Publicacions Matemàtiques

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Every (continuous) selection for the non-empty 2-point subsets of a space X naturally defines an interval-like topology on X. In the present paper, we demonstrate that, for a second-countable zero-dimensional space X, this topology may fail to be first-countable at some (or, even any) point of X. This settles some problems stated in [7].