INTRODUCTION TO SMOOTH MANIFOLDS by John M. Lee University of Washington Department of Mathematics John M. Lee Introduction to Smooth Manifolds Version 3.0 December 31, 2000 iv John M. Lee University of Washington Department of Mathematics Seattle, WA 98195-4350 USA lee@math.washington.edu http://www.math.washington.edu/~lee c 2000 by John M. Lee Preface This bo ok is an intro ductory graduate-level textbo ok on the theory of smo oth manifolds, for students who already have a solid acquaintance with general

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... x0 , y 0 ) X Ч Y 1 F (x, y ) X Ч Y , F (x, y 0 ) F (x0 , y 0 ) F (x0 , y ) x X y Y (1.1) , , max F (x, y 0 ) = F (x0 , y 0 ) = min F (x0 , y ). xX y Y . ... A = (aij )mЧn . ... 1) F (x, y ) X Ч Y ,  1. , max inf F (x, y ) = min sup F (x, y ). xX y Y y Y xX 5 (1.3) 2) (1.3). (x0 , y 0 ) , x0 - , y 0 - . ... 1.3. min aij -4 2 2 -3 1j4 1i4 7 -1 -4 1 4 2 3 2 A= 2 2 5 2 4 -3 7 -2 max aij 7 2 7 2 , , , . ... 8. : max min fi (xi ) = min fi (x0 ). i xX 1 i n 1in (8.1) 30 min fi (xi ), .. 1in . ...

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