Abstract
We recall that a topological space Y is called a Hausdorff space if its diagonal Δy is closed in Y x Y. An equivalent formulation of this concept is provided by the following characterization: a topological space Y is a Hausdorff space if for every topological space X and subset M of X, whenever two continuous functions f, g: X → Y agree on M, they must also agree on the topological closure of M.
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© 2003 Springer Science+Business Media New York
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Castellini, G. (2003). Separation. In: Categorical Closure Operators. Mathematics: Theory & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8234-7_12
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DOI: https://doi.org/10.1007/978-0-8176-8234-7_12
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6504-7
Online ISBN: 978-0-8176-8234-7
eBook Packages: Springer Book Archive