Does the axes of $\mathbb R^n$ have the fixed-point property?

Question

I was studying Croom's Principles of Topology and was asked to decide whether the set $$A=\{(x_1,x_2)\in\mathbb R^2:x_1=0\text{ or }x_2=0\}$$ has the fixed-point property. I first thought about scaling and rotating, but they all had the origin as a fixed point. So I'm confused if I'm supposed to show that $A$ has the fixed-point property, or I should try harder to come up with a counterexample. Any help would be appreciated.

Fixed-point property. A space $A$ has the fixed-point property if any continuous function $f:A\to A$ has a point $x\in A$ such that $f(x)=x$.

Answer 1

Let $f : A \to A, f(x_1,x_2) = (x_1+1,0)$. This map does not have a fixed pioint.