Can an open set in $\mathbb{R}^n$ homeomorphic to a non-open set?
126463
Can open sets and closed sets of $\mathbb{R}^n$ be homeomorphic?
16654
Unions and Intersections of Open Sets are Open
91878
Homeomorphism of the Disk
2677
Baire: Show that $f\colon \mathbb{R}\to\mathbb{R}$ is a polynomial in an open bounded set
36921
An Open Interval and a Half-open Interval are not Homeomorphic
83446
bijective continuous function on $\mathbb R^n$ not homeomorphism?
84104
Definition of neighborhood and open set in topology
155794
Are the complements of two homeomorphic compact, connected subsets of $\mathbb{R}^2$ homeomorphic?
41872
Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$
60053
Does the boundary of an open set have measure zero (in $\mathbb{R}^n$)?
25256
When a lattice is a lattice of open sets of some topological space?
129081
Proof that convex open sets in $\mathbb{R}^n$ are homeomorphic?
93750
Can a set be neither open nor closed?
70264
Prove that the inverse image of an open set is open
30079
Is for open connected $U$ the set $U_\varepsilon$ for small $\varepsilon$ connected?
99236
Interior of closure of an open set
20383
True or False: there is a space $X$ such that $S^1$ is homeomorphic to $X\times X$