Do we keep Path-connected => Connected?

[Jianing-Song]

Now we have $\sigma$-connected => connected and path-connected => $\sigma$-connected. Of course, the proof of path-connected => connected is much simpler than path-connected => $\sigma$-connected, so it is a question of keeping " $T_2\Rightarrow T_1$ ".

[prabau]

Like you said, it's similar to keeping [T2 ==> T1]. I am not going to push for removal, but we could discuss it in the Oct 4 zoom meeting. @StevenClontz ?

[StevenClontz]

I'm inclined to keep the direct implication.