Please, answer me that how is the set of all bounded invertible operators (for example on a Hilbert space) clopen (closed and open) in the set of all bounded surjective operators? In fact, which topology do imply this?
The relation between bounded invertible and surjective operators
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functional-analysis
operator-theory
hilbert-spaces
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0Did you manage to show that the set of invertible operators is open? – 2012-09-25
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0(I meant, for classical operator norm) – 2012-09-25