Definition Suppose $X$ is a topological space. Then $X$ is called ladder connected provided that any open cover $\mathcal{U}$ of $X$ has the following property: If $p,q\in X$ , then there exists a finite number of open sets $U_1,\ldots, U_N$ from $\mathcal{U}$ such that $p\in U_1$ , $U_1\cap U_2\neq \emptyset$ , $\ldots$ , $U_{N-1}\cap U_N\neq\emptyset$ , and $q\in U_N$ .