Homotopy & the Fundamental Group Flashcards
1
Q
path
A
continuous map from [0,1] to X that goes from γ(0) to γ(1)
2
Q
connected
A
can’t be written as disjoint union of non-trivial open sets
3
Q
path-connected
A
there exists a path between all points in x
4
Q
locally path-connected
A
in all open neighbourhoods there exists a path connected open neighbourhood
5
Q
based homotopic paths
A
there exists continuous F, with F(t,i)=γi(t) , F(i,0)=γi(0), F(i,1)=γi(1)
6
Q
based homotopy classes
A
Path(X,x,y)
7
Q
product/join of paths
A
α followed by β at double speed
8
Q
loop
A
path with the same starting and ending point
