Please can you check my proof of only clopen sets in $\mathbb R$ is $\mathbb R$ and $\varnothing$
11405
If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
70264
Prove that the inverse image of an open set is open
42145
Prove that the only sets in $R$ which are both open and closed are the empty set and $R$ itself.
56728
Question about limit points of a Subset of $\mathbb{R}$
62911
Let $(X,\tau)$ be a connected topological space, $Y\subset X$ connected and $U\subset X\setminus Y$ clopen. Prove that $ Y \cup U$ is connected
101669
Cardinality of the Set of all finite subset of $\mathbb{R}$
79424
Don't understand proof that interior of a set is open
47
Let $f$ be a continuous and open map from $\mathbb R $ to $\mathbb R$.Prove that $f$ is monotonic.
59424
Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
114608
Proof concerning regular space: there exist a closed set contained in any open set containing $x$
62755
The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
135814
Prove certain subsets of $\mathbb R^n$ are subspaces
44704
familly of Radially open sets in $\mathbb{R}^2$
131082
Proof that $\mathbb R/[0,1]$ and $\mathbb R$ are homeomorphic
136106
Is every open subset of $ \mathbb{R} $ uncountable?
138283
$|(a,b)| = |\Bbb R|$ ? Cardinality of any open interval
32441
How to prove or disprove statements about sets