By G. Coeuré (Eds.)

ISBN-10: 0080871224

ISBN-13: 9780080871226

ISBN-10: 0444106219

ISBN-13: 9780444106216

Coeure G. Analytic features and manifolds in endless dimensional areas (NHMS, NH, 1974)(ISBN 0444106219)

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**Sample text**

V v and C w) u w . It i s easy t o v e r i f y t h a t in c l u d e d i n w ( 1 / 2 . V 1 is ; t h e n we have c o n s t r u c t e d a n a d m i s s i b l e c o v e r i n g o f describes . Corollary 4 . 4 . - I f Z i s Banach space and E i s metriaable, any natural Frechet space i n b x ( X , Z l can be continuously imbedded i n t o a natural 8 . i. d . Frechet spaceJ that i s a c l a s s o f type Aa with an admissible and countable covering of x u . P r o o f . It i s a n o b v i o u s consequence o f theorem 2 .

V. s . For any open, b a l a n c e d , neighbourhood in X , the and E is a metrizable OE of V E , and any s e t f o l l o w i n g 'tboundaryt' f u n c t i o n s are d e f i n e d : V d (x) X V d (TI X SUP {r >/ b inf dX(x) [ %*+-rV V x c T is c o n t a i n e d i n X 1 . Definition 4 . 3 . - Let r be a s e t i n ~,(x,z); t h e s e t T f o r r i s defined by : 3 r i = { X E x [ [ [ f ( z ~ lll lf l ~ l , aZZ T-huZZ o f a bounding f cr 1 . Let 'l be a e. i. d, natura2 Frechet space i n 6xt~,~). Then T i n the I'-maximaZ extension ?

Given a f i n i t e dimensional, a f f i n e , subspace H , in E p-'(H) is a m n i f o l d spread over H which w i l l be denoted a s X H , The m n i f o l d IX,p) w i l l be called pseudoconvex whenever X H i s a Sbein m n i fold f o r any H L(E, 2) i8 the s e t of continuous endomorphism8 porn E i n t o 2 , . - I f X is the maximal extension of a s e t A i n and A is invariant by derivation and contains t h e mppings u o p u E L(E, 2) , then X any a i n t h e a d j o i n t space describes 1.

### Analytic Functions and Manifolds in Infinite Dimensional Spaces by G. Coeuré (Eds.)

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