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By J. Mujica

This complaints quantity comprises papers of study of expository nature, and is addressed to analyze staff and complicated graduate scholars in arithmetic. a few of the papers are the written and accelerated texts of lectures introduced on the convention, while others were incorporated by way of invitation.

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Theory J . BLATTER and L . SCHUMAKER, 38 ( 1 9 8 3 ) , 7 1 - 80. I6 1 A. L . BROWN, On c o n t i n u o u s s e l e c t i o n s f o r m e t r i c p r o j e c t i o n s i n s p a c e s o f continuous f u n c t i o n s . J. Ebnct. Anal. 8 (1971) , 431- 449. M E T R I C P R O J E C T I O N S OF c [ 7 ] A. J. LAZAR, D. E. WULBERT and P. D. MORRIS, C o n t i n u o u s s e l e c t i o n s f o r m e t r i c p r o j e c t i o n s . J. Funct. Anal. 3 (19691, 193 [ 8 - 216. 1 E. A. MICHAEL, C o n t i n u o u s s e l e c t i o n s 361 [ 9 ] 55 I .

J. Funct. Anal. 3 (19691, 193 [ 8 - 216. 1 E. A. MICHAEL, C o n t i n u o u s s e l e c t i o n s 361 [ 9 ] 55 I . Ann. of Math. 63 (1956), - 382. P. D. MORRIS, M e t r i c p r o j e c t i o n s onto s u b s p a c e s o f f i n i t e c o d i m e n s i o n . Duke Math. J. 35 (1968), 799 -808. [lo1 M. lecti:ons of p r o j e c t i o n f o r a c l a s s of weak C h e b y s h e v s p a c e s . Math. Anal. 13 (1982), 280 - 294. the metric SIAM J.

LsupprGl) are at most one-dimensional vector sublattices of C ( s u p p ( G ' ! ) ) and we conclude, using the result of Lazar, Morris and Wulbert in Section 1 and the fact that vanish off s u pp(Gl/, that the P: have conall elements of :G tinuous selections 5;. Appealing now to ( 3 ) we have that s = b ' + s"I + ... + s; is a continuous selection for P. (5) With the existence part now out of the way, we turn to the uniqueness part of our theorem. Suppose G is different from I 0 1 and c . If d z m G = I, then by the first Blatter and Schumaker result in G = B g Section 1, P possesses a unique continuous selection iff with g as claimed.

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