re: Math
@socks I mean you can have a connected clopen set, right? just take the set of all complex numbers with magnitude less than 1, in addition to all complex numbers with magnitude equal to one and positive real part (so, the unit disk, minus its boundary on the left half)
...or is that neither closed nor open? i think it would be either neither or both but i forget how exactly they're defined
-F
re: Math
@socks oh! huh
-F
re: Math
@Felthry Any subset itself is always going to be both closed and open _in its own topology_, though, by definition of subspace topology. Just not as a subset of the larger space
re: Math
@socks I don't think I undersatnd the concept of "in its own topology"! but we are too sleepy to really learn about it right now, maybe tomorrow, for now goodnight
-F
re: Math
@Felthry That is neither closed nor open with Euclidean topology
The DEFINITION of a connected space is one that doesn't have a proper subset that is both closed and open