Stone Spaces

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Cambridge University Press, Aug 14, 1986 - Mathematics - 370 pages
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Over the last 45 years, Boolean theorem has been generalized and extended in several different directions and its applications have reached into almost every area of modern mathematics; but since it lies on the frontiers of algebra, geometry, general topology and functional analysis, the corpus of mathematics which has arisen in this way is seldom seen as a whole. In order to give a unified treatment of this rather diverse body of material, Dr Johnstone begins by developing the theory of locales (a lattice-theoretic approach to 'general topology without points' which has achieved some notable results in the past ten years but which has not previously been treated in book form). This development culminates in the proof of Stone's Representation Theorem.
  

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Contents

I
1
II
11
III
15
IV
25
V
35
VI
39
VII
48
VIII
62
XXI
169
XXII
181
XXIII
191
XXIV
206
XXV
220
XXVI
224
XXVII
233
XXVIII
246

IX
69
X
76
XI
80
XII
92
XIII
98
XIV
111
XV
119
XVI
123
XVII
130
XVIII
142
XIX
152
XX
164
XXIX
253
XXX
267
XXXI
270
XXXII
286
XXXIII
297
XXXIV
308
XXXV
321
XXXVI
324
XXXVII
364
XXXVIII
366
XXXIX
368
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