Proving subset is not connected iff there exist open sets in X
123149
Prove that $E$ is disconnected iff there exists two open disjoint sets $A$,$B$ in $X$
79424
Don't understand proof that interior of a set is open
28641
Suppose $Y\subset X$ and $X,Y$ are connected and $A,B$ form separation for $X-Y$ then, prove that $Y\cup A$ and $Y\cup B$ are connected
136108
Arbitrary intersection of closed, connected subsets of a compact space connected?
147013
Subset of a finite set is finite
16654
Unions and Intersections of Open Sets are Open
3896
A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
153934
How to prove that a set R\Z is open
6291
Proving something is a linearly independent subset
88301
What are all of the connected subsets of $\mathbb{Q}$?
156520
Intervals are connected and the only connected sets in $\mathbb{R}$
72556
Is the closure of path-connected set path connected?
93623
Showing that every connected open set in a locally path connected space is path connected
151719
Connected set in $\mathbb{S}^1$
85225
The set of integers is not open or is open
39746
How to prove that given set is a connected subset of the space of matrices?
116932
Proving a simple graph is a connected graph