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    Quotients of Metric Spaces

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    Herman_1968.pdf (65.11Mb)
    Issue Date
    1968
    Author
    Herman, Robert A.
    Publisher
    The University of Kansas
    Format
    66 pages
    Type
    Thesis
    Degree Level
    M.A.
    Discipline
    Mathematics
    Rights
    This item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author.
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    Abstract
    The question of when a given property of a topological space is preserved under mappings is one of the most familiar problems of general topology. Among the properties of greatest interest for general spaces is, without doubt, that of metrizability; metrizability always implies, in particular, a number of important special topological properties of the space in question (normality, regularity, paracompactness, etc.). To determine in general the conditions for preservation of metrizability under mappings appears to be a difficult problem. It may well be that in the class of arbitrary continuous mappings the problem has no meaningful solution. The purpose of this paper is to obtain conditions for the preservation of metrizability under mappings appears to be a difficult problem. It may well be that in the class of arbitrary continuous mappings the problem has no meaningful solution. The purpose of this paper is to obtain conditions for the preservation of metrizability by quotient mappings and to study the properties of quotient spaces of metric spaces. We will use "iff" as an abbreviation for "if and only if". If f is a function from X onto Y, we will write f: X --->> Y.
    URI
    http://hdl.handle.net/1808/11166
    Collections
    • Theses [3797]
    • Mathematics Dissertations and Theses [180]
    • Mathematics Dissertations and Theses [180]

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    785-864-8983
    KU Libraries
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    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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