$H_0(X,A) = 0 \iff A$ meets each path-component of $X$.
35631
$H_0(X,A) = 0 \iff A \cap X_i \neq \emptyset \forall $ path-components $X_i$
50645
Is the following set (path) connected?
67088
Closure and pathwise connected
61274
If $AA^T$ is the zero matrix, then $A$ is the zero matrix
15865
Show that $X = \{ (x,y) \in\mathbb{R}^2\mid x \in \mathbb{Q}\text{ or }y \in \mathbb{Q}\}$ is path connected.
122213
Proving that if $\langle Ax,x\rangle =0$ for every $x$, then $A$ is the zero operator
105852
How to verify whether or not there exists a vector $x$ such that $Ax > 0$?
53236
Formal proof of $\lim_{x\to a}f(x) = \lim_{h\to 0} f(a+h)$
33822
Is there a monoid structure on the set of paths of a graph?
151168
dist$(x,A)=0$ if and only if $x\in \overline{A}$ (closure of $A$)
76790
Condition to guarantee $f=0$ on $[a,b]$
101778
Show that there is $\eta\in(0,1)$ with $f''(\eta)=f(\eta)$
63442
Show that if $U$ is an open connected subspace of $\mathbb{R}^2$, then $U$ is path connected
123753
In a metric $(X,d)$, prove that for each subset $A$, $x\in\bar{A}$ if and only if $d(x,A)=0.$
56446
A kind of converse of Lagrange's Theorem
86518
Does $X$ have a lower bound?
93623
Showing that every connected open set in a locally path connected space is path connected