Hey im looking for an exmaple of an isomorphism f between normed Spaces, where the inverse is not continous. I found some examples for continous bijective functions but its hard to imagine an example which is also linear. Thanks for your help.
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3You are leaving off a lot of information. You have, presumably, a function $f:A\to B$, yes? What are $A,B$? Sets, groups, topological spaces, topological groups, vector spaces, something else? – lulu Nov 17 '19 at 13:13
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1I also never saw a witch which was also linear. – Moishe Kohan Nov 17 '19 at 13:14
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sorry, f must be a funktion from X to Y, where X and Y are normed spaces – emily20 Nov 17 '19 at 13:35
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1Then add this information to your question. – Paul Frost Nov 17 '19 at 13:43
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https://en.wikipedia.org/wiki/Open_mapping_theorem_(functional_analysis) and https://math.stackexchange.com/questions/1060042/show-that-the-open-mapping-theorem-requires-both-spaces-to-be-complete – Moishe Kohan Nov 17 '19 at 13:48
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This may help https://math.stackexchange.com/questions/190707/two-lie-groups-which-are-isomorphic-but-not-homeomorphic – Javi Nov 17 '19 at 14:25