The Permutation Topological Spaces and their Bases


Given a permutation in the symmetric group on letters, we present permutation topological space and others new concepts in topology field such as sets, permutation subspace , permutation continuous, decomposition, connected. In this paper we prove that every permutation space is an Lindelof space. Moreover, we prove that, if the spaces are permutation topological spaces. Then the product permutation topology on has a countable base, and we give a number of examples