Continuous maps & the Fundamental Group

Question 1

push-forward

Answer 1

from loop based at x, to loop based on φ(x)

Question 2

homotopic continuous maps

Answer 2

there exists continuous map F: X x I–>Y
s.t. F(x,0)=φ0(x) F(x,1)=φ1(x)

Question 3

homotopic relative to A

Answer 3

restriction of φ0 to A is equal to restriction of φ1 to A

Question 4

homotopy equivalent spaces

Answer 4

there exist continuous maps φ and ψ that are inverses (both sides)

Question 5

retract

Answer 5

there exists continuous map r: X –> A st r(a)=a for all a and r is left inverse of the inclusion

Question 6

retraction

Answer 6

map r

Question 7

deformation retract

Answer 7

ior is homotopic to idx relA

Question 8

simply connected

Answer 8

path connected & trivial fundamental group

Question 9

contractible

Answer 9

homotopy equivalent to a singleton set