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My apology in advance if my question is elementary

According to the initial definition of topological stable rank introduced by Marc Rieffel we have the following:

An algebra has tsr 1 if the space of left invertible element is dense equivalently the space of right invertible elements is dense but why this is equivalent the space of invertible elements is a dense subset?

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  • $\begingroup$ Left invertibles dense actually implies that every left invertible is invertible. $\endgroup$
    – მამუკა ჯიბლაძე
    Commented Mar 24, 2023 at 16:51
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    $\begingroup$ Reference: B. Nica, Homotopical stable ranks for Banach algebras (J. Funct. Anal. 261, 2011), Proposition 3.5 $\endgroup$
    – მამუკა ჯიბლაძე
    Commented Mar 24, 2023 at 16:56
  • $\begingroup$ @მამუკაჯიბლაძე That is a very excellent reference, thank you very much for that! $\endgroup$
    – Ali Taghavi
    Commented Mar 24, 2023 at 17:26
  • $\begingroup$ @მამუკაჯიბლაძე I can not find your home page and your email address. I would appreciate if you send me an email to my yahoo email "[email protected]". Thank you $\endgroup$
    – Ali Taghavi
    Commented Apr 6, 2023 at 11:16

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