Proof follows immediately using Toronto, since something being inj path connected (and non discrete) implies it has card at least c.
Same with arcconnected ~and locally (1/n)-euclidean I think. EDIT: Actually there should be an implication ~discrete + Locally Euclidean + card = c => Toronto, since euclidean spaces are not toronto, see #1754
Proof follows immediately using Toronto, since something being inj path connected (and non discrete) implies it has card at least c.
Same with arcconnected ~and locally (1/n)-euclidean I think. EDIT: Actually there should be an implication ~discrete + Locally Euclidean + card = c =>
Toronto, since euclidean spaces are not toronto, see #1754