This article is cited in 2 papers

On a countable base and the conjugate class of a topological space

P. L. Ul'yanov


Abstract: In this paper the classes $\varphi (L)$ of functions are studied, and the topological spaces $U_\varphi$ are constructed from them. In particular, a necessary and sufficient condition guaranteeing a countable base in $U_\varphi$ is found. Classes $\overline\varphi (L)$ of functions conjugate (relative to sum) to $\varphi (L)$ are introduced and investigated.
Bibliography: 7 titles.

UDC: 517.512

MSC: 28A20, 54C35, 54A25

Received: 15.01.1976

 English version: Mathematics of the USSR-Sbornik, 1976, 29:1, 13–33

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