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categories: function spaces

Dear Comprox and Categories members,

Here is a short note that Reinhold Heckmann and I have written. Your
comments are welcome, as always.

                     On function spaces in topology

    It is the purpose of this expository note to provide a
    self-contained, elementary and brief development of the fact that
    the exponentiable topological spaces are precisely the
    core-compact spaces. The only prerequisite is a basic knowledge of
    topology (continuous functions, product topology and compactness).
    We hope that teachers and students of topology will find this
    useful. As far as we know, there is no such development available
    in the literature.  Although there are one or two embellishments,
    our methods are certainly not original.  We briefly discuss more
    advanced treatments in the introduction.

Best regards,
Martin & Reinhold