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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 $X$?

Hyperspace
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    How modest of you not to propose "hyperspace" :) – Trevor Wilson Oct 16 '12 at 23:01
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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). – Qiaochu Yuan Oct 16 '12 at 23:12
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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. – roman Oct 17 '12 at 08:12
  • @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? – Mark S. Jan 01 '14 at 16:20

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If $X$ is a subspace of $Y$, then $Y$ is usually called the ambient space of $X$.

roman
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