Definition of "homeomorphic"

Any infinite-dimensional Fréchet space homeomorphic with its countable product is topologically a Hilbert space.

1974, Wesley E. Terry, Transactions of the American Mathematical Society, volume 196, pages 93–104

A Vitali set can be homeomorphic to its complement.

2007, Andrjez Nowik, Acta Mathematica Hungarica, volumes 115:1-2, pages 145–154

A pair of non-homeomorphic product measures on the Cantor set.

2007, Tim D. Austin, Mathematical Proceedings of the Cambridge Philosophical Society, volume 142:1, pages 103–110