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MAST30026 Lecture 12: Function spaces (Part 2)

The aim of this lecture was to motivate the definition of the compact-open topology on function spaces, via the adjunction property. I explained how any topology making the adjunction property true must include a certain class of open sets, which we will define next lecture to be a sub-basis for the compact-open topology. Along the way we proved that evaluation and composition maps on function spaces are continuous. Lecture notes: http://therisingsea.org/notes/mast300... The class webpage: http://therisingsea.org/post/mast30026/ Have questions? I hold free public online office hours for this class, every week, all year. Drop in and say Hi! For details see the class webpage.