let S be Subset of ; :: thesis: ( S is empty implies S is arcwise_connected )
assume S is empty ; :: thesis: S is arcwise_connected
hence for x1, x2 being Element of st x1 in S & x2 in S holds
ex f being FinSequence of st
( f is continuous & rng f c= S & f . 1 = x1 & f . (len f) = x2 ) ; :: according to FINTOPO6:def 7 :: thesis: verum