Open subset of irreducible component is open in whole space if it doens't meet any other irreducible component.
58382
Open subscheme of an irreducible component remains open?
123149
Prove that $E$ is disconnected iff there exists two open disjoint sets $A$,$B$ in $X$
88823
How can the empty set be open in the definition of the cofinite topology?
108687
Open subsets in a manifold as submanifold of the same dimension?
113460
The only sets in $R^n$ which are both open and closed are the empty set and $R^n$ itself.
99341
Basic question: closure of irreducible sets
102250
Subset of $C[0,1]$ is nowhere dense
149317
An open subset of $\mathbb{R}$ is an at-most-countable union of disjoint open intervals
44431
The dimension of a subspace is less than dimension of the whole space.
44673
$M$ connected $\iff$ $M$ and $\emptyset$ are the only subsets of $M$ open and closed at the same time
129227
An example of neither open nor closed set
79424
Don't understand proof that interior of a set is open
74330
$\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
21599
$(0,1)$ is an open subset of $\mathbb{R}$ but not of $\mathbb{R}^2$, when we think of $\mathbb{R}$ as the x-axis in $\mathbb{R}^2$. Prove this.
40601
If a space $X$ has no isolated points, then nor does any dense subset of $X$.
101637
Let $R$ be an integral domain. If $x \in R$ is prime, then $x$ is irreducible.
78399
In $T_1$ space, all singleton sets are closed?