Proving that an open interval is an open set
135454
An open interval is an open set?
125233
Why is an open interval not a compact set?
6291
Proving something is a linearly independent subset
128987
A collection of pairwise disjoint open intervals must be countable
148507
Why an open set in $R^n$ might not be written as countable union of disjoint open intervals?
84104
Definition of neighborhood and open set in topology
73130
A simple question about open set
152976
Real Analysis: open and closed sets
47680
Prove that the union of the interior of a set and the boundary of the set is the closure of the set
148638
Write $(0,1)$ as a countable union of disjoint open intervals
59424
Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
73368
Does this proof that every open set in a metric space is a union of open balls use the axiom of choice?
138202
Every open set in $\mathbb{R}$ is a countable union of closed sets
38581
Construct a Borel set on R such that it intersect every open interval with non-zero non-"full" measure
108394
Proof of that every interval is connected
78786
Why does an open interval NOT have measure zero?
47
Let $f$ be a continuous and open map from $\mathbb R $ to $\mathbb R$.Prove that $f$ is monotonic.