Question on the existence of finite open subsets in $\mathbb{R}^{k}$
136106
Is every open subset of $ \mathbb{R} $ uncountable?
158498
$A\subset \mathbb{R}$ with more than one element and $A/ \{a\}$ is compact for a fixed $a\in A$
107160
Open Set and Measure Theory
61064
Finite index subgroup $G$ of $\mathbb{Z}_p$ is open.
73154
Compact subset in colimit of spaces
113915
A star shaped open set in $\mathbb{R}^n$ is diffeomorphic to $\mathbb{R}^n$
66334
How is every subset of the set of reals with the finite complement topology compact?
69499
Let $A\subset\mathbb{R}$ a measurable and bounded set. Show that exists for each $0\alpha$.
105445
Are the rationals a closed or open set in $\mathbb{R}$?
80180
Discrete and compact subset must be finite
153934
How to prove that a set R\Z is open
111538
If $S \subseteq X$ is closed, is $f(S,r)$ necessarily closed?
78422
Calculate the number $o(\mathbb{R})$ of open subsets of the real line.
126463
Can open sets and closed sets of $\mathbb{R}^n$ be homeomorphic?
18334
Equivalence between CH and existence of certain sets in $\mathbb{R}^2$
78117
Closed property of nonempty finite set
70048
In which topologies do open sets maintain open under countable or arbitrary intersection?