If $A, B$ are open dense subsets of a metric space $X$, is their intersection dense??
115625
Intersection of two open dense sets is dense
67702
Minimal dense subset
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
14048
Proof that the complement of zero-measure set on $[0,1]$ is dense in $[0,1]$
13132
If the union of two sets is contained in the intersection, then one is contained in the other ($[A\cup B\subseteq A\cap B]\implies A \subseteq B$)
6523
Prove that the space has a countable dense subset
134601
whether they are complete metric space
64487
Continuous function and dense set
123897
Sum of two open sets is open?
72468
Open and closed balls in $C[a,b]$
95831
Compactness and sequential compactness in metric spaces
114786
Question about Infimum. (conclusion about intersection)
44623
Closed set as a countable intersection of open sets
2978
A and B disjoint, A compact, and B closed implies there is positive distance between both sets
109046
Is the complement of an open ball in a Banach space connected?
22854
Let $A , B\subseteq\mathbb{R}$. If $A$ is closed and $B$ is compact, is $A\cdot B$ closed?
25256
When a lattice is a lattice of open sets of some topological space?