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Dominic van der Zypen
Dominic van der Zypen
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If $(X,\tau)$ is a $T_2$-space such that all non-empty open sets are homeomorphicall non-empty open sets are homeomorphic (with the subspace topology) to $X$, is $(X,\tau)$ necessarily homogeneous?

If $(X,\tau)$ is a $T_2$-space such that all non-empty open sets are homeomorphic (with the subspace topology) to $X$, is $(X,\tau)$ necessarily homogeneous?

If $(X,\tau)$ is a $T_2$-space such that all non-empty open sets are homeomorphic (with the subspace topology) to $X$, is $(X,\tau)$ necessarily homogeneous?

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Dominic van der Zypen
Dominic van der Zypen
  • 48.8k
  • 8
  • 47
  • 161

Homeomorphic open sets and homogeneity

If $(X,\tau)$ is a $T_2$-space such that all non-empty open sets are homeomorphic (with the subspace topology) to $X$, is $(X,\tau)$ necessarily homogeneous?