Original Articles

EXPONENTIAL LAW AND θ-CONTINUOUS FUNCTIONS

Published in: Quaestiones Mathematicae
Volume 8 , issue 2 , 1985 , pages: 131–142

DOI: 10.1080/16073606.1985.9631907

Author(s): A. Di Concilio , ITALIA

Keywords: Primary , 54C35 , Secondary , 54C10 , 54B30 , 18B30 , Primary , 54C35 , Secondary , 54C10 , 54B30 , 18B30

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.

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