Can any one paint $\mathbb R^+$ with two colors which sum of two numbers with the same color has the same color. Additional condition: Both colors should be used. I tried use Cauchy functions like ...
Let $R$ be the ring of continuous functions from $[0,1]$ to the real numbers. Fix $c \in [0,1]$ and let $M_c$ = ker $E_c$ where $E_c$ denotes evaluation at $c$, a ring homomorphism from $R$ to the ...
So I just noticed that the set of functions with a fixed point $$f(x_0)=x_0,$$ are closed under composition $$(f*g)(x):=g(f(x)),$$ and with $e(x)=x$, the inverible functions even seem to form a ...