I'm starting to learn about path connected spaces and am a bit sketchy, any help would be appreciated, cheers,

Lets say i Have the set S = {0,1} with topology { emptyset, {0}, S }

and i need to prove S is path connected and therefore connected,

to show path connectedness,

i need to show a path exists from x to y for any x,y in S,

to show this i need a cotinuous map p : [0,1] -> S such that p(0) = x and p(1) = y

im confused how to do this for this set,