Why must $A(V)$ be an open subset of $A$'s range?
38033
A surjective linear map into a finite dimensional space is open
102924
Normal space- equivalent condition: $\forall U, V$ - open $: U \cup V = X \ \ \ \exists F \subset U \ , G \subset V$ - closed $: F \cup G = X$
3896
A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
50506
What concept does an open set axiomatise?
84104
Definition of neighborhood and open set in topology
64861
Intersection of open affines can be covered by open sets distinguished in *both*affines
102168
Prove that there exists disjoint open subsets $U,V$ of $X$ such that $x \in U$ and $B \subseteq V$.
143105
Show that, for every real number a, the set {$x ∈ S | f(x) ≤ a$} is a closed subset of $\mathbb R^d$
75829
Dimension of open subsets of $R^n$
152976
Real Analysis: open and closed sets
35305
Why is $\mathbb{R}^2$ not a subset and /or a subspace of $\mathbb{R}^3$?
9320
Extension of continuous function on a closed subset of $\mathbb{R}$
98634
What is a counterexample for If $x\in\overline{A},$ $x$ is not necessarily a limit of a sequence in $A$?
92639
Prove that the family of open sets in $\mathbb{R}$ has cardinality equal to $2^{\aleph_0}$
149317
An open subset of $\mathbb{R}$ is an at-most-countable union of disjoint open intervals
79424
Don't understand proof that interior of a set is open
105445
Are the rationals a closed or open set in $\mathbb{R}$?