The permutation topological spaces and their bases

الملخص EN

Given a permutation  in the symmetric group on n letters, we present permutation topological space ( , )  n  t and others new concepts in topology field such as   sets, permutation subspace ( , )    m  t , permutation continuous,   decomposition,   connected.

In this paper we prove that every permutation space is an Lindelof space.

Moreover, we prove that, if the spaces , ,...

1 2   are permutation topological spaces.

Then the product permutation topology on ...

1 2    has a countable base, and we give a number of examples.