In this paper we show that groups of transformations defined on antidiscrete topological spaces are the only ones among pseudogroups. It means that if a topological structure of a pseudogroup is the weakest then an algebraic structure of this pseudogroup is a group.
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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.
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In [1] it was shown how to obtain pseudogroups of functions from quasi-algebraic spaces which were introduced by W. Waliszewski. In [2] it was shown how to obtain pseudogroups from premanifolds. In this paper we show how to obtain pseudogroups from groups.
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