"A local property of the subspaces of Euclidean differential spaces"

with Kowalczyk Adam, Demostratio Mathematica, Vol. XI, No4, 1978, 875-885.
publications

Differential spaces in Sikorski's sense are considered. Any subset M Ě Rⁿ is considered as a differential subspace of the differential space (Rⁿ, C^Ą(Rⁿ)). It is proved the following theorem: For any p Î M Ě Rⁿ the integer m = dimT_pM is the smallest one such that there exists in M an open neighbourhood U of the point p which is included in an m-dimensional C ^Ą -surface of Rⁿ.
From this theorem we obtain as a corollary: any differential subspace of a differential space of the D_o class is a differential space of the D_o class, too.