Displaying similar documents to “Complemented subalgebras of the Baire-1 functions defined on the interval [ 0 , 1 ] .”

Isomorphism Problems for the Baire Function Spaces of Topological Spaces

Choban, Mitrofan (1998)

Serdica Mathematical Journal

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Let a compact Hausdorff space X contain a non-empty perfect subset. If α < β and β is a countable ordinal, then the Banach space Bα (X) of all bounded real-valued functions of Baire class α on X is a proper subspace of the Banach space Bβ (X). In this paper it is shown that: 1. Bα (X) has a representation as C(bα X), where bα X is a compactification of the space P X – the underlying set of X in the Baire topology generated by the Gδ -sets in X. 2. If 1 ≤ α < β ≤ Ω, where...

Baire spaces

R. C. Haworth, R. A McCoy

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CONTENTSIntroduction............................................................................................................ 5I. Basic properties of Baire spaces................................................................... 61. Nowhere dense sets............................................................................................... 62. First and second category sets............................................................................. 83. Baire spaces................................................................................................................

Compactness in the First Baire Class and Baire-1 Operators

Mercourakis, S., Stamati, E. (2002)

Serdica Mathematical Journal

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For a polish space M and a Banach space E let B1 (M, E) be the space of first Baire class functions from M to E, endowed with the pointwise weak topology. We study the compact subsets of B1 (M, E) and show that the fundamental results proved by Rosenthal, Bourgain, Fremlin, Talagrand and Godefroy, in case E = R, also hold true in the general case. For instance: a subset of B1 (M, E) is compact iff it is sequentially (resp. countably) compact, the convex hull of a compact bounded subset...

Unordered Baire-like spaces without local convexity.

Jerzy Kakol, Walter Roelcke (1992)

Collectanea Mathematica

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The aim of the present paper is to study the class of tvs which we define by ommiting the word increasing in the definition of *-suprabarrelled spaces. We prove that the product of Baire tvs is *-UBL and hence the class of *-UBL spaces is stricty larger than the class of Baire spaces.

Baire-like spaces C(X,E)

Jerzy Kakol (2000)

Revista Matemática Complutense

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We characterize Baire-like spaces C(X,E) of continuous functions defined on a locally compact and Hewitt space X into a locally convex space E endowed with the compact-open topology.