“Boundedly generated topological spaces”
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The new class of Boundedly generated topological spaces (or l-spaces) is defined and studied by topological methods. It is shown that it is strictly broader than the class of (Hausdorff) compactly generated spaces (or k-spaces) and also that l-spaces possess many of the nice properties of k-spaces e.g. they are closed under the formation of disjoint unions, quotients, direct limits e.t.c. The topology of uniform convergence on boundeda is also studied and in general, it is shown to be strictly finer than the compact-open topology on the space of continuous functions.
KeywordsContinuous Function Topological Space Number Theory Algebraic Geometry Disjoint Union
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