I was reading Spivak's Calculus on Manifolds and in chapter 1, section 2, dealing with compactness of sets he mentions that it is "easy to see" that if [itex] B \subset R^m [/itex] and [itex] x \in R^n [/itex] then [itex]\{x\}\times B \subset R^{n+M}[/itex] is compact. While it is certainly plausible, I can't quite get how to handle set products when dealing with covers.(adsbygoogle = window.adsbygoogle || []).push({});

I was wonering if anyone could sketch a proof of this for me, I've been stuck on that page for days now.

note: this is not homework, just doing some self study.

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# Compactness of point and compact set product

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