Table Of Contents:

I COMPACT SETS IN FUNCTION SPACES 1(60)

1 Topology of pointwise convergence 3(5)

2 A theorem of Eberlein 8(4)

3 Ptak's Lemma 12(5)

4 Namioka's theorem 17(3)

5 Rosenthal's dichotomy 20(5)

6 Properties of Baire and Ramsey 25(4)

7 Baire property of analytic sets 29(3)

8 Baire property of filters and ideals 32(3)

9 Selective coideals 35(6)

10 Baire's characterization theorem and its corollaries 41(5)

11 Borel sets 46(3)

12 A selective analytic ideal 49(6)

13 Bourgain-Fremlin-Talagrand's theorem 55(4)

References for Chapter I 59(2)

II THE SEMIGROUP Beta(N) 61(18)

14 A space of ultrafilters 63(4)

15 Glazer's Theorem 67(4)

16 A topological proof of the van der Waerden theorem 71(4)

17 A semigroup of variable words 75(3)

References for Chapter II 78(1)

III COMPACT AND COMPACTLY GENERATED GROUPS 79(42)

18 Countable chain conditions of topological groups 81(6)

19 Michael's selection theorem 87(4)

20 Inverse systems 91(4)

21 Haydon's theorem 95(4)

22 Quotient groups 99(6)

23 A decomposition of compact groups 105(4)

24 Pestov's theorems 109(4)

25 Free topological groups 113(6)

References for Chapter III 119(2)

IV HYPERSPACES 121(25)

26 Exponentially complete spaces 123(4)

27 Vaught's homeomorphism theorem 127(3)

28 Resolving a space: Accumulation orders and spectra 130(5)

29 Accumulation spectra of hyperspaces 135(4)

30 List of all exponentials 139(2)

31 Multiplication of accumulation orders 141(5)
References for Chapter IV 146(3)
Index 149(3)
Index of special symbols 152