On the number closure-type mappings

In this paper, we consider mappings of Cartesian powers $S^n$ of an arbitrary partially ordered set $S$ into itself which possess the main properties of closures. For each partially ordered set, we describe the asymptotic behaviour of the logarithm of the number of such mappings as $n\to\infty$.
This research was supported by the Russian Foundation for Basic Research, grant 03–01–00783.