- #1

iLoveTopology

- 11

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But now, if we have a topological space that is just one component, (it is connected), and there is a closed curve in it that is not orientation preserving (so T is not orientable) it doesn't seem like there should be a way to "remove" a piece so that T is now orientable.

Am I off base in this assumption? I am having a hard time finding theorems that will help me prove or disprove this because most the theorems I have in my book have to do with compact spaces and I don't want this to depend on compactness.