Topics in Topology

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.