Original title: Homogenita topologických struktur
Translated title: Homogeneity of topological structures
Authors: Vejnar, Benjamin ; Hušek, Miroslav (advisor) ; Pyrih, Pavel (referee)
Document type: Master’s theses
Year: 2009
Language: eng
Abstract: In the present work we study those compacti cations such that every autohomeomorphism of the base space can be continuously extended over the compacti cation. These are called H-compacti cations. We characterize them by several equivalent conditions and we prove that H-compacti cations of a given space form a complete upper semilattice which is a complete lattice when the given space is supposed to be locally compact. Next, we describe all H-compacti cations of discrete spaces as well as of countable locally compact spaces. It is shown that the only H-compacti cations of Euclidean spaces of dimension at least two are one-point compacti cation and the Cech-Stone compacti cation. Further we get that there are exactly 11 H-compacti cations of a countable sum of Euclidean spaces of dimension at least two and that there are exactly 26 H-compacti cations of a countable sum of real lines. These are all described and a Hasse diagram of a lattice they form is given.

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/23307

Permalink: http://www.nusl.cz/ntk/nusl-494784


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Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Master’s theses