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This is a very short question, I hope it is not too broad, if so I shall try and make it more specific. I would like to start as it stands below, though, because it really points down the essence of the question:

What do people mean when they write that a map is extended by continuity ?

Thanks !

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    @MartinWanvik: I am trying to find an example that has not been answered by the comments of Robert and Alex above - though at the moment it seems I might have mixed things up in my head because I cannot find one. I'll edit the post in case I find one !2012-04-19

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