FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2003, VOLUME 9, NUMBER 4, PAGES 41-54

On soft mappings of the unit ball of Borel measures

Yu. V. Sadovnichii

Abstract

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The main result of this paper is two theorems. One of them asserts that the functor $U$_t takes the $0$-soft mappings between spaces of weight $$£ w₁ and Polish spaces to soft mappings. The other theorem, which is a corollary to the first one, asserts that the functor $U$_t takes the $AE(0)$-spaces of weight $$£ w₁ to $AE$-spaces. These theorems are proved under Martin's axiom $MA($w₁).

The results cannot be extended to spaces of weight $$³ w₂. For spaces of weight $$w₁, these results cannot be obtained without additional set-theoretic assumptions. Thus, the question as to whether the space $U$_t(R^w₁) is an absolute extensor cannot be answered in ZFC.

The main result cannot be transferred to the functor $U$_R of the unit ball of Radon measures. Indeed, the space $U$_R(R^w₁) is not real-compact and, therefore, $U$_R(R^w₁) Ï AE(0).

Location: http://mech.math.msu.su/~fpm/eng/k03/k034/k03402h.htm.
Last modified: September 24, 2004.