Recent Progress in General Topology III - Hart, K.P.; van Mill, J.; Simon, P.; SpringerLink (Online service) (Paris : Atlantis Press : Imprint: Atlantis Press, 2014)
The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 2002. The following areas experienced significant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.
Topological Homogeneity -- Some Recent Progress Concerning Topology of Fractals -- A biased view of topology as a tool in functional analysis -- Large scale versus small scale -- Descriptive aspects of Rosenthal compacta -- Minimality conditions in topological groups -- Set-Theoretic update on Topology -- Topics in Dimension Theory -- Representations of dynamical systems on Banach spaces -- Generalized metrizable spaces -- Permanence in Coarse Geometry -- Selections and Hyperspaces -- Continuum Theory -- Almost disjoint families and topology -- Some Topics in Geometric Topology II -- Topological aspects of dynamics of pairs, tuples and sets -- Continuous selections of multivalued mappings -- The combinatorics of open covers -- Covering properties -- Paratopological and semitopological groups vs topological groups.
Keywords: Mathematics; Topological Groups; Functional analysis; Logic, Symbolic and mathematical; Topology; Mathematics; Topology; Topological Groups, Lie Groups; Functional Analysis; Mathematical Logic and Foundations