If $f$ is the quotient mapping, is $(Y,\tau_1)$ metrizable?
69528
Metrizability of quotient spaces of metric spaces
144521
Why does Möbius transformation $f(z)$ map the unit disk $|z|<1$ to itself?
134199
Holomorphic function mapping a set onto a straight line
71037
Is exponential map locally a diffeomorphism w.r.t. base point?
52729
Homotopic maps $(X, A) \to (Y, B)$ induce homotopic maps $X/A \to X/B$
95887
How to show that quotient space $X/Y$ is complete when $X$ is Banach space, and $Y$ is a closed subspace of $X$?
133884
A proof using Yoneda lemma
63104
Dual cone of $K = \{(x,t) \mid \| \boldsymbol{x} \|_1 \le t \}$
121957
Is $p\mapsto \|f\|_p$ continuous?
153492
Let $p\colon X \to Y$ be a quotient map then if each set $p^{-1}({y})$ is connected, and if $Y$ is connected, then $X$ is connected.
139779
Homotopic maps have homotopy equivalent mapping cones
119256
Function $f\in M[G]$, $f:\kappa\to M$ is in the ground model implies $\kappa^+$-Baire
143043
When is a local homeomorphism a covering map?
67234
The function $G: x \mapsto 2^{x^2}$ maps $\mathbb{R}$ onto $\{ x \in \mathbb{R} : x \geq 1 \}$
101893
Is there a classification of regular maps $\mathbb{P}^1(k)\to\mathbb{A}^1(k)$?
106298
Prove that some topology is not metrizable
150379
Perfect Map $p:\ X\to Y$, $Y$ compact implies $X$ compact