= Solution
{c}
A <metric space> $(X,d)$ is a <complete metric space> if every <Cauchy sequence> in $X$ converges to a point of $X$. Explicitly, the hypothesis is
$$
\forall\varepsilon>0\ \exists N\ \forall m,n\geq N:\ d(x_m,x_n)<\varepsilon,
$$
and the conclusion is that some $x\in X$ satisfies $d(x_n,x)\to0$.
It is a <sequentially compact space> if every <sequence> in $X$ has a <convergent subsequence> whose <limit of a sequence> belongs to $X$.
It is a <connected space> if there are no disjoint nonempty <open subsets> $U,V$ of $X$ with $X=U\cup V$. Here openness refers to the <metric topology> of $X$.
It is a <path-connected space> if, for every $x,y\in X$, there is a <continuous map> $\gamma:[0,1]\to X$ with $\gamma(0)=x$ and $\gamma(1)=y$. Such a map is a <path>. Every <path-connected space> is a <connected space>: a separation would pull back along a <path> joining its two sides to a separation of the <interval> $[0,1]$.
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