An Effective Tietze-Urysohn Theorem for QCB-Spaces: (Extended Abstract)

The Tietze-Urysohn Theorem states that every continuous real-valued function defined on a closed subspace of a normal space can be extended to a continuous function on the whole space. We prove an effective version of this theorem in the Type Two Model of Effectivity (TTE). Moreover, for qcb-spaces we introduce a slightly weaker notion of normality than the classical one and show that this property still admits an Extension Theorem for continuous functions.