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- W3023341493 abstract "Publisher SummaryThis chapter discusses some longstanding open problems about the structure of homogeneous compacta. The fact that these questions are all stated in very simple topological terms fully demonstrates that there is still a lot of work to be done in this area. Many of the familiar classical objects in topology are homogeneous: manifolds without boundary, the Cantor set, the rational numbers, the irrational numbers, the universal Menger continua, the Hilbert cube and connected manifolds modeled on it, the pseudoarc, the circle of pseudoarcs, and topological groups. Besides topological groups and large products of the spaces mentioned, most of the examples of homogeneous spaces are metrizable. Homogeneity is best understood in the presence of metrizability and it plays a significant role there. Outside the class of metrizable spaces, homogeneity is not a well-understood notion. There are many theorems that imply that certain spaces are inhomogeneous, quite often based on delicate cardinality considerations. The Rudin's problem, Van Douwen's problem, and Arhangel'skiĭ's problem are also discussed in the chapter. A detailed discussion on continuous images of homogeneous compacta is also presented." @default.
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- W3023341493 date "2007-01-01" @default.
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- W3023341493 title "Homogeneous compacta" @default.
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- W3023341493 doi "https://doi.org/10.1016/b978-044452208-5/50021-1" @default.
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