Does any nonempty open set in $\mathbb{R}^n$ contains a point with rational coordinates?
92740
prove that $\mathbb{Q}^n$is dense subset of $\mathbb{R^n}$
103717
Topological Property of the Set of Integers
2882
Limit points of the set $\{\frac {\varphi(n) }n : n\in \mathbb{N}\}$
152451
REVISITED $^2$: Does a solution in $\mathbb{R}^n$ imply a solution in $\mathbb{Q}^n$?
47975
Closed cone in the euclidean space $\mathbb{R}^n$
66272
Is there a common notion of $\mathbb{R}^n$, for non-integer $n$?
41611
Open and closed set in n by n matrices space.
92639
Prove that the family of open sets in $\mathbb{R}$ has cardinality equal to $2^{\aleph_0}$
38033
A surjective linear map into a finite dimensional space is open
22464
Which of the following subsets of   $\mathbb{R}^2$ are compact
69283
The limit points of an open interval (open set)
116542
Which of the following sets are compact in $\mathbb{M}_n(\mathbb{R})$[NBHM_PhD Screening Test-2013, Topology]
101979
Set of open intervals in R with rational endpoints is a basis for standard topology on R
324
Show uncountable set of real numbers has a point of accumulation
91736
Explicit homeomorphism between open and closed rational intervals?
127575
Prove that Open Sets in $\mathbb{R}$ are The Disjoint Union of Open Intervals Without the Axioms of Choice
67259
Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?