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This is more of a linguistic question than a mathematical one, but let me try anyway:

What is the antonym of subspace?

Is it a superspace? What else?

Suppose $X$ is a subspace of $Y$, say, a topological space, a vector space or whatever other spaces there are in mathematics. What is then $Y$ in relation to $X$?

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    How modest of you not to propose "hyperspace" :)2012-10-16
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    "Superspace" is probably a bad idea; "super" already has connotations coming from supersymmetry (see for example http://en.wikipedia.org/wiki/Supermanifold).2012-10-16
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    I'd go with _ambient space_, and wikipedia supports that opinion: http://en.wikipedia.org/wiki/Ambient_space - anyway, I've never really seen someone use this term.2012-10-17
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    @roman Would be be interested in posting some variation of your comment as an answer, so that this no longer remains on the unanswered page?2014-01-01

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