[일반] graph가 path connected면 continuous인가요?

[익명(106.102)]

function f: X -> Y의 graph G = {(x, f(x)) | x in X}에 X × Y의 subspace topology를 줬을 때, G가 path connected라면

f는 항상 continuous인가요?

[카카오M(kakaothh)]

https://math.stackexchange.com/questions/3954664/continuous-if-and-only-if-graph-of-every-path-connected-subspace-is-path-connect

[익명(106.102)]

흑흑 고맙읍니다