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2005•Zeitschrift für Analysis und ihre AnwendungenOpen access

Vector Valued Baire Functions

H. R. Shatery, J. Zafarani

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Abstract

In this paper, we study some properties of the Banach space β • α (X, E), consists of all Baire functions with relatively compact ranges from a perfectly normal space X into a Banach space E.Moreover, we establish that if β • α (X, E) is linear isometric with β • α (Y, E), then some compactification of X and Y are homeomorphic.

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What this paper is about

In this paper, we study some properties of the Banach space β • α (X, E), consists of all Baire functions with relatively compact ranges from a perfectly normal space X into a Banach space E.Moreover, we establish that if β • α (X, E) is linear isometric with β • α (Y, E), then some compactification of X and Y are homeomorphic.

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Available abstract

In this paper, we study some properties of the Banach space β • α (X, E), consists of all Baire functions with relatively compact ranges from a perfectly normal space X into a Banach space E.Moreover, we establish that if β • α (X, E) is linear isometric with β • α (Y, E), then some compactification of X and Y are homeomorphic.

Key concepts: Compactification (mathematics), Mathematics, Banach space, Baire space, Baire category theorem, Pure mathematics, Baire measure, Infinite-dimensional vector function

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