Form equivalence class Howard-Rubin Number: 1

Statement:

If \((X,T)\) is a \(T_4\) topological space and \(U =\{U_i: i\in K\}\), \(|U_i|\ge 2\), is a locally finite family ofopen non-empty pairwise disjoint sets, then there is a continuous real valued function \(f\) on \(X\) which assumes at least two distinct values on each \(U_i\).

Howard-Rubin number: 1 BW

Citations (articles): Keremedis [1997] Continuous real valued functions in \(T_4\) spaces

Connections (notes): Note [43]

These are definitions from Brunner [1982b] and results similar to the equivalence of [8 C] and [8 D] to Form 8 and [10 H] to Form 10. We also include some results from Brunner [1987b].


References (books):

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