ladder connected

DefinitionSuppose $X$ is a topological space. Then$X$ is called ladder connected provided that anyopen cover $𝒰$ of $X$ has the following property:If $p,q\in X$, then there exists a finite number ofopen sets $U_1,\mathrm{\dots },U_N$ from $𝒰$ such that$p\in U_1$, $U_1\cap U_2\ne \mathrm{\varnothing }$, $\mathrm{\dots }$ , $U_{N-1}\cap U_N\ne \mathrm{\varnothing }$,and $q\in U_N$.