42
votes
1answer
1k views

What is the algebraic structure of functions with fixed points?

So I just noticed that the set of functions with a fixed point $$f(x_0)=x_0,$$ are closed under composition $$(f\circ g)(x):=g(f(x)),$$ and with $e(x)=x$, the inverible functions even seem to form ...
2
votes
2answers
235 views

What does the word “ideal” mean in this context?

I'm confused about a terminology. In Frank W. Warner's book Foundations of Differentiable Manifolds and Lie Groups, it says on page 12 Let $F_m$, a subset of $\bar{F_m}$ (the set of germs at ...