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.