By Jens Peter Reus. Christensen
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Additional info for Topology and Borel Structure: Descriptive topology and set theory with applications to functional analysis and measure theory
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Nm TH€ V] u [ E ( (ml, Bk contains Ak (we a l s o make use of condition 1) ). B : We a l s o have another r e p r e s e n t a t i o n o f OD 4 1 ‘V , m v ) ) Ima N ,1 5 mi ini ,i=l,, v i t follows by the use o f since defined by B ‘lo B = u f / vI= Ei ( ( m l , . 3 . Evidently m P e Nvp m? ,m: )). But i t then f o l l o w s c l e a r l y t h a t for all k. From the f i r s t r e p r e s e n t a t i o n of B we can see t h a t B 6 fg ,while the second r e p r e s e n t a t i o n shows t h a t As e > 0 , B4A . Then there exist B1,B2t a ( Y ) by the topology Indeed,let (the Borel structure generated Blfl B2 =0 and ) such that g:h@-+A1 and 'OD h:N - jA2 AiC Bi i=1,2. be continuous and THEOKEMS 01: StPARATION, I