Controlling Tietze-Urysohn extensions

An Effective Tietze-Urysohn Theorem for QCB-Spaces

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, we introduce for qcb-spaces a slightly weaker notion of normality than the classical one and show that this prop...

An Analysis of the Lemmas of Urysohn and Urysohn-Tietze According to Effective Borel Measurability

Classboxes: controlling visibility of class extensions

A class extension is a method that is defined in a module, but whose class is defined elsewhere. Class extensions offer a convenient way to incrementally modify existing classes when subclassing is inappropriate. Unfortunately existing approaches suffer from various limitations. Either class extensions have a global impact, with possibly negative effects for unexpected clients, or they have a p...

A Tietze Transformation Program

A Reidemeister-Schreier program which yields a presentation of a subgroup H of finite index in a finitely presented group G is described in [3J. The program has two stages; first, Schreier generators and Reidemeister relators for H are computed, then the resulting presentation is simplified by eliminating redundant generators and by using a substring searching technique. The Tietze transformati...

Weakly Continuously Urysohn Spaces

We study weakly continuously Urysohn spaces, which were introduced in [Z]. We show that every weakly continuously Urysohn w∆-space has a base of countable order, that separable weakly continuously Urysohn spaces are submetrizable, hence continuously Urysohn, that monontonically normal weakly continuously Urysohn spaces are hereditarily paracompact, and that no linear extension of any uncountabl...