It follows from 

> I. M. Dektjarev, A closed graph theorem for ultracomplete spaces, Dokl. Akad. Nauk. Sov., 154 (1964), 771–773 (in Russian).

See also discussion on p. 5 [here][2].


  [1]: http://matwbn.icm.edu.pl/ksiazki/sm/sm2/sm211.pdf
  [2]: https://arxiv.org/pdf/1707.02624.pdf