Talk:Continuous Surjection Induces Continuous Bijection from Quotient Space/Corollary 1

I think there's a good argument for:
 * Let $T_1 = \struct {S_1, \tau_1}$ and $T_2 = \struct {S_2, \tau_2}$ be topological spaces

that is, keeping the $T_1$ and $T_2$.

Reason: you would then discuss:
 * Let $g: T_1 \to T_2$ be a continuous surjection.

Continuity is not relevant until you take the topology into account. Hence you need to specify the mapping as to be from and to the structures that include that topology.

Otherwise if $S_1 = S_2$ (and they only differ by their topologies) then saying: "Let $g: S_1 \to S_1$ ... etc. loses its meaning.

Thoughts? --prime mover (talk) 22:39, 23 September 2022 (UTC)