Brilliant framing of quasi-homeomorphisms through the quotient map lens. The way this reframes Property 3a by showing U = f⁻¹[f[U]] when dealing with topologically indistingusihable points really clicked for me. I once got stuck tryingto prove something similiar in a measure theory context, and seeing the connection to equivalence relations would've saved me hours. The unit cirlce example nails why we care about codomain versus range too.
Brilliant framing of quasi-homeomorphisms through the quotient map lens. The way this reframes Property 3a by showing U = f⁻¹[f[U]] when dealing with topologically indistingusihable points really clicked for me. I once got stuck tryingto prove something similiar in a measure theory context, and seeing the connection to equivalence relations would've saved me hours. The unit cirlce example nails why we care about codomain versus range too.
Thanks!