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:

The following forms are listed as conclusions of this form class in rfb1: 1,

Back