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May 17th, 2017, 07:11 AM   #1
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Isomorphic spaces

I stumbled upon this symbol ≅ and I found out it stands for isomorphism. Can anybody explain what it means for a space D to be isomorphic to R (D ≅ R) ?
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May 17th, 2017, 08:34 AM   #2
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Two spaces $A$ and $B$ are isomorphic if there exists a bijective map $\phi : A \rightarrow B$. If two spaces are isomorphic then it means they are similar but labeled differently. Check this out https://en.wikibooks.org/wiki/Linear...f_Isomorphisms
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May 18th, 2017, 03:57 AM   #3
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What kind of "spaces" are you talking about? If they are "vector spaces" (or "linear spaces) in linear algebra, then that bijection must also "preserve the operations". That is, .
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May 18th, 2017, 10:07 AM   #4
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An isomorphism is a bijective map which preserves structure.
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