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Post Reopened by YCor, R.P., Pace Nielsen, Will Brian, András Bátkai
Post Closed as "Duplicate" by Lee Mosher, Chris Godsil, Ben McKay, CommunityBot
changed senseless title
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YCor
YCor
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Is R Homeomorphic characterization of the only space homeomorphic to this spacereal line?

Let $A$ be a path connected-connected subset of $\mathbb R^2$ such that the removal of any singleton from $A$ splits $A$ into two open connected components, each of which is path connected-connected.

Is $A$ necessarily homeomorphic to $R$$\mathbb{R}$?

Is R the only space homeomorphic to this space?

Let $A$ be a path connected subset of $\mathbb R^2$ such that the removal of any singleton from $A$ splits $A$ into two open connected components, each of which is path connected.

Is $A$ necessarily homeomorphic to $R$?

Homeomorphic characterization of the real line?

Let $A$ be a path-connected subset of $\mathbb R^2$ such that the removal of any singleton from $A$ splits $A$ into two open connected components, each of which is path-connected.

Is $A$ necessarily homeomorphic to $\mathbb{R}$?

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James Baxter
James Baxter
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Is R the only space homeomorphic to this space?

Let $A$ be a path connected subset of $\mathbb R^2$ such that the removal of any singleton from $A$ splits $A$ into two open connected components, each of which is path connected.

Is $A$ necessarily homeomorphic to $R$?