What is $\Bbb E$?
I believe this is just alternative notation for $\Bbb R$ where $\Bbb R$ is assumed to have the standard Euclidean topology. Is this correct?
Is seems to be used in this way in Armstrong's Basic topology
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I've seen $\mathbb{E}$ used to denote $\mathbb{R}^n$ where $n$ is left unspecified. However, I'm not sure how Armstrong is using it. – Kevin Jun 03 '15 at 06:26
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@Kevin He is making mention ot $\Bbb E^3$ for example and treating it like $\Bbb R^3$, but I am not certain that there are no differences. But I think you may be right, $\Bbb E$ may be a general way of referring to any number of dimensions on $\Bbb R^n$ – Exam in 5 days Jun 03 '15 at 06:27
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I thought it was used so that there was no ambiguity in which metric you are using. So $E$ would denote the standard euclidean metric. – Mr.Fry Jun 03 '15 at 06:53
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@Mr.Fry That was what I thought, thanks. – Exam in 5 days Jun 03 '15 at 06:55
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Are you asking specifically about the usage in Armstrong's book?. Or somewhere else (like your lecture notes or test from past exams)? – Martin Sleziak Jun 03 '15 at 07:20
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@MartinSleziak Generally terminology I suppose. But the question came from reading Armstrong, which just starts talking about $\Bbb E$ I believe on page 12 with "Let $f$ be a function between two euclidean space, say $f: \Bbb E^m \to \Bbb E^n$ – Exam in 5 days Jun 03 '15 at 07:28
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Here is a related question: What differences are between $\mathbb{E}^n$ and $\mathbb{R}^n$ – Martin Sleziak Jun 03 '15 at 07:35