Show that $\pi_1: X \times Y \to X$ is an open map
38019
Projection is an open map
66531
$\|h(x)-h(y)\|\geq 3\|x-y\|$ prove that image of open is open
88155
Show that $[0, 1)\times[0, 1)$ is homeomorphic to $[0, 1]\times[0, 1)$ but not to $[0, 1]\times[0, 1]$.
57816
$(S^1 \times [0,1])/\sim$ homeomorphic to unit disk $ D^2$
52354
Given a idempotent endomorphism, show that $M = \ker(f) \oplus \ker (f-\text{id}_M)$
7890
Prove the map $\Phi:G\to\operatorname{Aut}G$ with $g\mapsto (x\mapsto g^{-1}xg)$ is an homomorphism.
39455
Prove that $(X\times Y)\setminus (A\times B)$ is connected
15095
continuous onto map from $(0,1)\to (0,1]$
60485
Show that $S^1 - \lbrace (1,0)\rbrace$ is homeomorphic to the open interval $(0,1)$
127575
Prove that Open Sets in $\mathbb{R}$ are The Disjoint Union of Open Intervals Without the Axioms of Choice
75829
Dimension of open subsets of $R^n$
52388
The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition
78344
Nonconstant linear functional on a topological vector space is an open mapping
149999
fixed point of a continuous map on a projective space
131082
Proof that $\mathbb R/[0,1]$ and $\mathbb R$ are homeomorphic
79424
Don't understand proof that interior of a set is open
17607
Open maps which are not continuous