Topics in Topology

• Main Author: Todorcevic, Stevo (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1997.
• Edition: 1st ed. 1997.
• Series: Lecture Notes in Mathematics, 1652
• Subjects: Topology.; Topological groups.; Lie groups.; Functions of real variables.; Topological Groups, Lie Groups.; Real Functions.
• Physical Description: VIII, 160 p. online resource.
• ISBN: 9783540683384
• ISSN: 0075-8434 ;
• DOI: 10.1007/BFb0096295

The book describes some interactions of topology with other areas of mathematics and it requires only basic background. 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 hyperspaces of compact metric zerodimensional spaces.