AbstractIn this paper, we discuss the nonlinear functional spaces based on triangular conorms. Particularly, we discuss the properties of the upper-closures of the regular subspaces of the nonlinear functional space based on a continuous triangular conorm. Furthermore, we prove that with respect to a strict triangular conorm, a subset of the nonlinear functional space is an upper-complete normal subspace if and only if the family of all sets whose characteristic functionals are contained in the given subset of the nonlinear functional space is a sigma-algebra.