# AMS Student Chapter Seminar: Difference between revisions

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Title: | Title: [[Media:Compact-openTalk.pdf|The compact open topology: what is it really?]] | ||

Abstract: The compact-open topology on the space C(X,Y) of continuous functions from X to Y is mysteriously generated by declaring that for each compact subset K of X and each open subset V of Y, the continous functions f: X->Y conducting K inside V constitute an open set. In this talk, I will explain the universal property that uniquely determines the compact-open topology, and sketch a pretty constellation of little-known but elementary facts from domain theory that dispell the mystery of the compact-open topology's definition. | Abstract: The compact-open topology on the space C(X,Y) of continuous functions from X to Y is mysteriously generated by declaring that for each compact subset K of X and each open subset V of Y, the continous functions f: X->Y conducting K inside V constitute an open set. In this talk, I will explain the universal property that uniquely determines the compact-open topology, and sketch a pretty constellation of little-known but elementary facts from domain theory that dispell the mystery of the compact-open topology's definition. |

## Revision as of 05:41, 25 September 2014

**General Information**: AMS Student Chapter Seminar will take place on Wednesday at 3:30 in the 9th floor lounge area. Talks should be of interest to the general math community, and generally will not run longer than 30 minutes. Everyone is welcome to give a talk, please just sign up on this page. Alternatively we will also sign interested people up at the seminar itself. There will generally be bagel provided, although the snack may vary from week to week.

To sign up please provide your name and a title. Abstracts are welcome but optional.

## Fall 2014

## Wednesday, September 25, Vladimir Sotirov

Title: The compact open topology: what is it really?

Abstract: The compact-open topology on the space C(X,Y) of continuous functions from X to Y is mysteriously generated by declaring that for each compact subset K of X and each open subset V of Y, the continous functions f: X->Y conducting K inside V constitute an open set. In this talk, I will explain the universal property that uniquely determines the compact-open topology, and sketch a pretty constellation of little-known but elementary facts from domain theory that dispell the mystery of the compact-open topology's definition.