Prove that an open interval $(a,b)$ considered as a subspace of a real line is homeomorphic to the real line.
6118
Homeomorphism of the real line-Topology
150796
Subspace topology and order topology (2)
62118
Prove $\epsilon$-$\delta$ definition of continuity implies the open set definition for real function
27998
Prove existence of disjoint open sets containing disjoint closed sets in a topology induced by a metric.
82458
Homeomorphism between the unit disc and the unit square
66531
$\|h(x)-h(y)\|\geq 3\|x-y\|$ prove that image of open is open
139979
Proof there is a rational between any two reals
27855
Show that $(a,b)\times (c,d)$ is an open set in $\mathbb{R}^2$ with the Euclidian metric.
125233
Why is an open interval not a compact set?
15560
Prove that the union of three subspaces of $V$ is a subspace iff one of the subspaces contains the other two.
114608
Proof concerning regular space: there exist a closed set contained in any open set containing $x$
157597
Homeomorphism between $\mathbb{Q}$ and $\mathbb{Q}(>0)$, and $\mathbb{Q}(\ge 0)$
102168
Prove that there exists disjoint open subsets $U,V$ of $X$ such that $x \in U$ and $B \subseteq V$.
124786
Prove that V contains a subspace of each dimension
146445
What Topology does a Straight Line in the Plane Inherit as a Subspace of $\mathbb{R_l} \times \mathbb{R}$ and of $\mathbb{R_l} \times \mathbb{R_l}$
66691
Real function continuous on closed interval implies it is bounded - over-simple proof??
83166
Homeomorphism(topological spaces) version of Cantor–Bernstein–Schroeder theorem