Form equivalence class Howard-Rubin Number: 1

Statement:

For every infinite cardinal \(\kappa\), if \((X,T)\) is a \(T_2\) space having a base \(B\) such that no \(Q\subseteq B\), \(|Q| <\kappa\), is a tower, then for every family \(\cal D=\{D_i:i\in\kappa\}\) of dense open sets of \(X\) there is a filter \(F\subseteq T\) such thatfor every \(i\in\kappa\) there  is a \(b\in F\) with \(b\subseteq D_i\).

Howard-Rubin number: 1 CB

Citations (articles): Keremedis [1998a] Filters, antichains and towers in topological spaces and the axiom of choice

Connections (notes): Note [77] In this note we include definitions from Keremedis [1998a] for forms [1 BL] through [1 BR], [1CB], and [67 G].

References (books):

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