How many path-connected components does $O_{2}(\mathbb{R})$ have?
My Attempt: I believe that the answer is 2, but I'm not sure how to work with the definition and describing the path-connected components.
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Can you think of a continuous map to a space with two path connected components? – Bubaya May 10 '19 at 06:01
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@Carmeister It is not a perfect duplicate of your link (components vs. path components), but the answer covers the present question. – Paul Frost May 10 '19 at 12:07