prove the connectedness of a set
112731
If $Y$ is connected, why is $A\cup Y$ connected in this case?
4776
Prove that the power set of an $n$-element set contains $2^n$ elements
72556
Is the closure of path-connected set path connected?
111008
Show that $X $ is a infinite set ,it is connected in the finite complement topology?
34099
Proving that the empty set is unique
37183
Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
90590
Prove that the following set is dense
118595
Proving that a set is countable by finding a bijection
144383
The closure of a connected set in a topological space is connected
36878
Prove that $\operatorname{SL}(n,\Bbb R)$ is connected.
66948
Proving question on sets
136158
$X$ has Indiscrete topology $\implies$ any subset of $X$ is connected
108394
Proof of that every interval is connected
35115
Questions on how to prove that a set of connectives is NOT functionally complete
146364
$X$ is connected iff $\forall A\subset X,$ $\partial A\neq\emptyset$
109682
Proposed proof of: If $A \subset B \subset \bar{A}$ and $A$ is connected, then $B$ is connected
58285
Is it true that if $X$ is connected, then for every nonempty proper subset $A$ of $X$, we have $\mathbf{Bd} \ne \emptyset$