9

Part of 1994 Miklós Schweitzer

Problems(1)

Source: miklos schweitzer 1994 q9

Let X be a dense set homeomorphic to

\mathbb R^n

in the compact Hausdorff space Y. Prove that for

n\geq 2

Y \setminus X

is connected, and for n=1 it consists of at most two components.