Abstract The category θ-Top of topological spaces and θ-continuous functions is not Cartesian closed; but it is known that under certain local property assumptions, the exponential law in θ-Top is fulfilled. We define a functor from θ-Top to the category of H-θ-topological spaces and prove that in this category the exponential law holds without any local property assumptions. We also provide a functor from θ-Top to Katětov's category of filter-merotopic spaces, which is Cartesian closed. A.M.S. 1980 subject classification: Primary, 54C35, Secondary, 54C10, 54B30, 18B30
Exponential law and theta-continuous functions
DI CONCILIO, Anna
1985-01-01
Abstract
Abstract The category θ-Top of topological spaces and θ-continuous functions is not Cartesian closed; but it is known that under certain local property assumptions, the exponential law in θ-Top is fulfilled. We define a functor from θ-Top to the category of H-θ-topological spaces and prove that in this category the exponential law holds without any local property assumptions. We also provide a functor from θ-Top to Katětov's category of filter-merotopic spaces, which is Cartesian closed. A.M.S. 1980 subject classification: Primary, 54C35, Secondary, 54C10, 54B30, 18B30File in questo prodotto:
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