TABLE OF CONTENTS THE PROBLEM, METHODS OF ATTACK, DIFFICULTIES The representation problem for Freohet varieties . . . .5 The representation problem for Freohet surfaces 13 TOPOLOGICAL PRELIMINARIES Monotoneity and lightness 22 Peano spaoes 23 2-manifolds 25 Mantoids 27 V The Ceoh theory 31 The locally compact theory ..... 34 Cohomology theory of 2-manifolds and oanonioal regions . 38 Key theorems 43 COMPARABILITY AND CONSISTENCY Hyper elements 47 Normal and simple regions ... .48 Cohomology on hyper elements 52 Compatibility &2 THE NECESSITY ARGUMENT The case for 2-manifolds with boundary . 71 The case for closed 2-manifolds .81
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