showing that $\Phi:\Pi_{1}(X,x_{0})\rightarrow [S^{1},X]$ is onto if $X$ is path connected.
127365
Question on showing a bijection between $\pi_1(X,x_0)$ and $[S^1, X]$ when X is path connected.
42811
Product of path connected spaces is path connected
106585
Show $d_{1}(x_{n},x)\rightarrow{0}$ if and only if $d_{2}(x_{n},x)\rightarrow{0}$.
35069
Connectedness of the boundary
30079
Is for open connected $U$ the set $U_\varepsilon$ for small $\varepsilon$ connected?
102598
Show that $X$ is path connected if and only if each $X_\alpha$ is path connected.
35236
Proof $p \vdash q \Rightarrow p$
72556
Is the closure of path-connected set path connected?
82448
Why is $f(x) = x\phi(x)$ one-to-one?
64993
Connectedness of the $S^2$ sphere
4602
Outline of a proof that $\mathbb{R}^2 - A$ where A is countable is path-connected
127919
prove that if $E$ is connected and $E \subseteq F \subseteq \overline{E}$, then $F$ is connected.
89164
When is the graph of the divisor relation on $[n]$ planar?
120971
(Revised) Prove that $\phi$ is a group homomorphism and find the kernel.
35631
$H_0(X,A) = 0 \iff A \cap X_i \neq \emptyset \forall $ path-components $X_i$
58642
If $g \circ f$ is the identity function, then which of $f$ and $g$ is onto and which is one-to-one?
158582
Prove that $\{\frac{\phi (n)}{n}\}_{n \in \Bbb N}$ is dense in $[0,1]$