>>60
Not
>>58 here, but being homotopic to a constant function is also often called null-homotopic.
Basically a function f is homotopic to a function g
f,g:X -> Y (spaces X and Y)
if there exists a continuous function H: X x [0,1] -> Y
s.t H(x,0) = f(x) H(x,1) = g(x)
I've not used this definition at all, but I'd have thought any continuous function on the real line would be null-homotopic :-/
given f cts. let H(x,t) = f(x) - t.(f(x)-1)
H(x,t) pretty trivially cts and H(x,0) = f(x) H(x,1) = 1
But this contradicts
>>58 since he said the extended function is not essential, whereas in fact the original function would not be essential, being undefined at a point. Whereas the extended function would be essential.
Odd.