Knaster-Reichbach Theorem for the generalized Cantor space

Notes (work in progress).

Classical Knaster-Reichbach Theorem states, that if $P,Q\subseteq 2^\omega$ are closed nowhere dense subsets of the classical Cantor space, and $h\colon P\to Q$ is a homeomorphism, then there exists a homeomorphism $H\colon 2^\omega\to 2^\omega$ such that $H\upharpoonright P=h$ .

In this note we present an analogue of Knaster-Richbach Theorem for the generalized Cantor space $2^\kappa$ . This answers an oral question of W. Kubiś.

Michał Korch

Knaster-Reichbach Theorem for the generalized Cantor space

Mathematics, set theory, travels, mountains