Statement:
Theorem of Goodner: A compact \(T_{2}\) space is extremally disconnected (the closure of every open set is open) if and only if each non-empty subset of \(C(X)\) (set of continuous real valued functions on \(X\)) which is pointwise bounded has a supremum.
Howard_Rubin_Number: 157
Parameter(s): This form does not depend on parameters
This form's transferability is: Unknown
This form's negation transferability is: Negation Transferable
Article Citations:
Goodner-1950: Projections in normed linear spaces
Book references
Note connections: