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The space of ANR’s in n

Tadeusz DobrowolskiLeonard Rubin — 1994

Fundamenta Mathematicae

The hyperspaces A N R ( n ) and A R ( n ) in 2 n ( n 3 ) consisting respectively of all compact absolute neighborhood retracts and all compact absolute retracts are studied. It is shown that both have the Borel type of absolute G δ σ δ -spaces and that, indeed, they are not F σ δ σ -spaces. The main result is that A N R ( n ) is an absorber for the class of all absolute G δ σ δ -spaces and is therefore homeomorphic to the standard model space Ω 3 of this class.

Applications of some results of infinite-dimensional topology to the topological classification of operator images

This volume consists of three relatively independent articles devoted to the topological study of the so-called operator images and weak unit balls of Banach spaces. These articles are: “The topological classification of weak unit balls of Banach spaces” by T. Banakh, “The topological and Borel classification of operator images” by T. Banakh, T. Dobrowolski and A. Plichko, and “Operator images homeomorphic to Σ ω ” by T. Banakh. The articles summarize investigations that has been done by these authors...

A contribution to the topological classification of the spaces Ср(X)

Robert CautyTadeusz DobrowolskiWitold Marciszewski — 1993

Fundamenta Mathematicae

We prove that for each countably infinite, regular space X such that C p ( X ) is a Z σ -space, the topology of C p ( X ) is determined by the class F 0 ( C p ( X ) ) of spaces embeddable onto closed subsets of C p ( X ) . We show that C p ( X ) , whenever Borel, is of an exact multiplicative class; it is homeomorphic to the absorbing set Ω α for the multiplicative Borel class M α if F 0 ( C p ( X ) ) = M α . For each ordinal α ≥ 2, we provide an example X α such that C p ( X α ) is homeomorphic to Ω α .

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