Let $X_1$ and $X_2$ be connected topological spaces. I want to show that the product $X_1 \times X_2$ is connected.
48557
Product of connected spaces
104411
sum of two connected subset of $\mathbb{R}$
82578
Show that if $G$ is $2-$connected, then for any two vertices $u$ and $v$ there exists a cycle $C$ such that $u, v \in V (C)$
123149
Prove that $E$ is disconnected iff there exists two open disjoint sets $A$,$B$ in $X$
150796
Subspace topology and order topology (2)
41690
Products of Continuous functions: Topology
134703
Let $X$ be a connected space, $f:X\to X$ continuous involution, $g:X\to\mathbb{R}$ continuous. Prove that $\exists$ $x\in X$ such that $g(x)=g(f(x))$.
111008
Show that $X $ is a infinite set ,it is connected in the finite complement topology?
31266
Proof of "the continuous image of a connected set is connected"
133633
A question about path-connected and arcwise-connected spaces
64619
Continuity of a function of product spaces
2575
Showing that $\mathbb{R}$ is connected
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
14713
$X=(-\infty,0]\cup\left\{{1\over n}:n\in\mathbb N\right\}$ with subspace topology Then
7665
If $h : Y \to X$ is a covering map and $Y$ is connected, then the cardinality of the fiber $h^{-1}(x)$ is independent of $x \in X$.
88155
Show that $[0, 1)\times[0, 1)$ is homeomorphic to $[0, 1]\times[0, 1)$ but not to $[0, 1]\times[0, 1]$.
77289
Example 2, Sec. 24, in Munkres' TOPOLOGY, 2nd ed: If $X$ is a well ordered set, then $X \times [0, 1)$ is a linear continuum