On the extension of the ring topology of a $\sigma$-bounded field to a simple transcendental extension of the field

V. I. Arnautov


Abstract: If $\tau$ is a ring topology of a field $R$ such that $(R,\tau)$ is the union of countably many bounded sets, then there exists a ring topology $\hat\tau$ on a simple transcendental extension $R[x]$ of $R$ such that $(R[x],\hat\tau)$ is the union of countably many bounded sets and $\tau$ is the restriction of $\hat\tau$ to $R$.
Bibliography: 6 titles.

UDC: 512.56

MSC: Primary 12J99, 54H13; Secondary 12F20

Received: 17.10.1985

 English version: Mathematics of the USSR-Sbornik, 1988, 61:2, 271–287

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