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Pseudogroups in premanifolds

Lipińska J.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2002

Vol. 1, nr 1

93--95

In [1] it was proved that the set of all diffeomorphisms of a quasi-algebraic space which was introduced by W. Waliszewski is the Ehresmann’s pseudogroup. Proving this theorem we did not use properties of a quasi-algebraic space, so it was possible to generalize this theorem and formulate it for any set of functions. It was noticed in [2]. The concept of an analytical premanifold was introduced by Waliszewski in [3]. In [4] he also called it a general differential space. In this paper we show how to use the above theorem in analytical premanifolds.