Let $A$ and $B$ be disjoint. Let $X$ be a topological space.
Is every continuous function $f:X=A \cup B \rightarrow \{-1,1\}$ constant?
Let $A$ and $B$ be disjoint. Let $X$ be a topological space.
Is every continuous function $f:X=A \cup B \rightarrow \{-1,1\}$ constant?