About contractible implies simply connected
97133
contractible and simply connected
34071
Contractive condition implies the sequence is Cauchy
39076
Contraction of compact sets
3649
Closed unit interval is connected proof
157218
If $E\subseteq X$ is connected, $E\cap A\neq\emptyset$ and $E\cap(X\setminus A)\neq\emptyset$ then $E\cap\partial A\neq\emptyset$
116494
What happens to the connectedness of $\mathbb R^2$ when countable many points are removed?
112731
If $Y$ is connected, why is $A\cup Y$ connected in this case?
147961
Characterizing simply connected spaces
10541
How to prove Mandelbrot set is simply connected?
153492
Let $p\colon X \to Y$ be a quotient map then if each set $p^{-1}({y})$ is connected, and if $Y$ is connected, then $X$ is connected.
17165
Is total boundedness a topological property?
42811
Product of path connected spaces is path connected
96781
connected manifolds are path connected
45337
Suppose that $V, W$ are closed in $X$ and that $V\cap W, V\cup W$ are connected. Show that $V$ and $W$ are connected.
142795
Is "connected, simply connected" Redundant?
23225
Union of connected subsets is connected if intersection is nonempty
127919
prove that if $E$ is connected and $E \subseteq F \subseteq \overline{E}$, then $F$ is connected.