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Aug 11, 2010 at 17:42 comment added Dylan Wilson Compactly generated is absolutely okay- the whole reason why algebraic topologists find the category convenient is because it is cartesian closed. And the topology in question is the compact-open one.
Aug 11, 2010 at 17:24 comment added Andrea Ferretti The answer to (1) is no: the exponential law is only valid for some nice topological spaces; for instance I think that compactly generated is ok.
Aug 11, 2010 at 17:16 history answered Jeff Strom CC BY-SA 2.5