Continuous map of pseudotopological spaces: Difference between revisions

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Latest revision as of 19:45, 24 November 2008

Definition

Suppose are pseudotopological spaces (with the usual abuse of notation of identifying a pseudotopological space with its underlying set). Suppose is a function. We say that is a continuous map of pseudotopological spaces if for any ultrafilter on and any point such that , we have:

In other words, the pushforward of converges to the image of . Here, we define as follows:

.