Describing some interactions of topology with other areas of mathematics, this text assumes only a basic knowledge of the subject. The first chapter deals with the topology of pointwise convergence and proves results of Bourgain, Fremlin, Talagrand and Rosenthal on compact sets of Baire class-1 functions. In the second chapter some topological dynamics of beta-N and its applications to combinatorial number theory are presented. The third chapter gives a proof of the Ivanovskii-Kuzminov-Vilenkin theorem that compact groups are dyadic. The last chapter presents Marjanovic's classification of hyper-spaces of compact metric zerodimensional spaces.
Contents: Topology of pointwise convergence.- A theorem of Eberlein.- Ptak's Lemma.- Namioka's theorem.- Rosenthal's theorem.- Properties of Baire and Ramsey.- Baire property of analytic sets.- Baire property of filters and ideals.- Selective coideals.- Baire's characterization theorem and its corollaries.- Borel sets.- A selective analytic ideal.- Bourgain-Fremlin-Talagrand's theorem.- A space of ultrafilters.- Glazer's theorem.- A topological proof of van der Waerden theorem.- A semigroup of variable words.- Countable chain conditions of topological groups.- Michael's selection theorem.- Inverse systems.- Haydon's theorem.- Quotient groups.- A decomposition of compact groups.- Pestov's theorems.- Free topological groups.- Exponentially complete spaces.- Vaught's homeomorphism theorem.- Resolving a space: Accumulation orders and spectra.- Accumulation spectra of hyperspaces.- List of all exponentials.- Multiplication of accumulation orders.
Series: Lecture Notes in Mathematics
Number Of Pages: 160
Published: 20th March 1997
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6
Weight (kg): 0.25