Prove that all contractible spaces are simply connected.
97133
contractible and simply connected
132641
Proving that Euclidean Space is a complete metric space
146364
$X$ is connected iff $\forall A\subset X,$ $\partial A\neq\emptyset$
93623
Showing that every connected open set in a locally path connected space is path connected
149980
Are there any countable Hausdorff connected spaces?
33527
Star convex set is simply connected.
39076
Contraction of compact sets
33859
How to show that a disjoint sum of metric spaces is metrizable?
116866
$A\times B$ connected component implies $A,B$ connect components
67050
Every separable metric space has a countable base
39746
How to prove that given set is a connected subset of the space of matrices?
35652
Every compact metric space is complete
69358
Given a simple graph and its complement, prove that either of them is always connected.
99645
Metrizable topological space $X$ with every admissible metric complete then $X$ is compact
144383
The closure of a connected set in a topological space is connected
62911
Let $(X,\tau)$ be a connected topological space, $Y\subset X$ connected and $U\subset X\setminus Y$ clopen. Prove that $ Y \cup U$ is connected
116932
Proving a simple graph is a connected graph