What is an example of an connected and homogeneous $ T_2$ -space $ (X,\tau)$ with $ |X|=2^{\aleph_0}$ such that for no $ n\in\mathbb{R}$ the space $ (X,\tau)$ is homeomorphic to a subspace of $ \mathbb{R}^n$ ?

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# Tag: homogeneous

## Connected and homogeneous $T_2$-space not homeomorphic to a subset of $\mathbb{R}^n$

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What is an example of an connected and homogeneous $ T_2$ -space $ (X,\tau)$ with $ |X|=2^{\aleph_0}$ such that for no $ n\in\mathbb{R}$ the space $ (X,\tau)$ is homeomorphic to a subspace of $ \mathbb{R}^n$ ?