Being entirely in different things at once

Sextus Empiricus in his Outlines, dealing with genus and its species, rips off an argument of the Parmenides. If we interpret the genus-species relation artificially in terms of ordinary geometric inclusion then obviously there will be problems.  But there is nothing contradictory about several objects $a_1,a_2,...,a_n$ all sharing the same relation with the same object $b$, i.e. $R(a_1,c), R(a_2,c),...,R(a_n,c)$. In fact they all share the same property $\lambda x. R(x,c)$. 

But what if we question set theoretic equality and replace it with path-connectedness ? For instance $x \subset y$ means that for every $z\in x$ we have that there is a continuous path $p_{zw}$ from $z$ to $w$ for some $w \in y$.  Then we can well have that $x_1,x_2...,x_n \subset y$ and at the same time $y\subset x_1,...,y \subset x_n$.

Consider the following set in the plane with the relative topology:

 Then by our definition we have that  $\{x_i\}\subset \{y\}$ and $\{y\}\subset \{x_i\}$ for $i=1,...,5$.

Also, what is a set of elements ? The elements must have a distinguishing property or relation prior to being organized into the set (this discussion needs to be greatly expanded).