On the number of topologies on countable skew fields

V. I. Arnautov ; G. N. Ermakova

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2020), pp. 63-74.

Résumé

If a countable skew field $R$ admits a non-discrete metrizable topology ${\tau }_0$, then the lattice of all topologies of this skew fields admits: – Continuum of non-discrete metrizable topologies of the skew fields stronger than the topology ${\tau }_0$ and such that $sup\{{\tau }_1,{\tau }_2\}$ is the discrete topology for any different topologies ${\tau }_1$ and ${\tau }_2$; – Continuum of non-discrete metrizable topologies of the skew fields stronger than ${\tau }_0$ and such that any two of these topologies are comparable; – Two to the power of continuum of topologies of the skew fields stronger than ${\tau }_0$, each of them is a coatom in the lattice of all topologies of the skew fields.

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