Let {$ X_i $: i $ \in $ I} be a family of topological spaces. Show that $ \prod_{i \in I} X_i $ is path-connected...
102598
Show that $X$ is path connected if and only if each $X_\alpha$ is path connected.
17470
Does path-connected imply simple path-connected?
126192
Connected, locally connected, path-connected but not locally path-connected subspace of the plane
129943
Torsion on $\pi_1(X)$, $X$ connected and open in $\mathbb{R}^n$
16512
Product of $T_1$ spaces is $T_1$
56440
Cartesian products and families
4602
Outline of a proof that $\mathbb{R}^2 - A$ where A is countable is path-connected
84437
Prove that the projection $p_i$ from the product space $X_I S_i \tau$ into $S_i \tau_i$ is open for each $i \in I$
47680
Prove that the union of the interior of a set and the boundary of the set is the closure of the set
15865
Show that $X = \{ (x,y) \in\mathbb{R}^2\mid x \in \mathbb{Q}\text{ or }y \in \mathbb{Q}\}$ is path connected.
48557
Product of connected spaces
112731
If $Y$ is connected, why is $A\cup Y$ connected in this case?
46970
If $X$ is compact and $T:X \to Y$ continuous and bijective, show that $T$ is homeomorphism.
102484
Connectedness problem and countability of compact subsets of the Sorgenfrey line
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.
102485
Showing that a topological space is ${\rm T}_1$
157830
Definition of locally pathwise connected