Prove that if $f:D^2\to D^2$ is a homeomorphism, then $f(S^1)=S^1$
91878
Homeomorphism of the Disk
81546
Prove that function from $S^n \times S^m \to 2S^{m+n+1}$ is immersion
27757
$\mathbb{R}\to\mathbb{R}$ Diffeomorphism with special property
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
27251
Holomorphic function with $f\circ f=f$
132311
T$\mathbb{S}^{n} \times \mathbb{R}$ is diffeomorphic to $\mathbb{S}^{n}\times \mathbb{R}^{n+1}$
31479
homeomorphism of cantor set extends to the plane?
34699
A continuous bijection from a compact space to a $T_2$ space is always a homeomorphism
13993
Can we prove $ℝ^n ∖ \{\text{straight line}\}$ and $ℝ^n ∖ \text{\{an axis\}}$ homeomorphic by proving their complements homeomorphic?
130872
Map $f: S^n \to S^n$ that extends over $D^{n+1}$ must identify a pair of antipodal points
2348
Show that the sphere, S, and $\mathbb{R}^2$ is not homeomorphic
88278
Show $S = f^{-1}(f(S))$ for all subsets $S$ iff $f$ is injective
27746
Autohomeomorphism of the unit disk which is constant on the boundary, and which takes 0 to a prescribed point
75863
how to prove $f^{-1}(B_1 \cap B_2) = f^{-1}(B_1) \cap f^{-1}(B_2)$
93471
Space of homeomorphisms Homeo$(S^1)$ of $S^1$ deformation retracts onto $O(2)$
143269
Existence of area-preserving diffeomorphism between two sets in $\mathbb{R}^2$
33050
proof that translation of a function converges to function in $L^1$