arXiv:2610.35912v1 Announce Type: new Abstract: Working with tools from infinite-dimensional topology and using measure-theoretic ideas we analyze numerous well-known fami\-lies of copu\-las and quasi-copulas from a topological perspective, prove that most of them are homeomorphic to the Hilbert cube $\mathcal{H}$ and hence have the Fixed Point as well as the Disjoint Cells property. Working with so-called $Z$-sets, we then study how large one set is within another. Doing so, in order to show that a set $A$ is small/topologically negligible within a compact metric space $(\Omega,m)$, we construct a homeomorphism $h: [0,1] \times \mathcal{H} \to \Omega$ mapping $\{0\} \times \mathcal{H}$ to $A$. The obtained results are to a certain extent surprising since various supposedly small families are topologically large.
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