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On a problem of L. Nachbin. (English) Zbl 0441.04002

Summary: If \(B\) is an uncountable set then there is a function \(r\colon B\times B\to\mathbb R_+\), for which there is no function \(t\colon B\to\mathbb R_+\) such that
\[ r(b_1,b_2) \leq t(b) \cdot t(b_2) \quad\text{for\;all }b_1,b_2\in B. \]

MSC:

03E10 Ordinal and cardinal numbers
46A03 General theory of locally convex spaces

Keywords:

uncountable set

Citations:

Zbl 0399.46034
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