A Generalization of Lie Theory: a Generalization of Main Theorems in Lie Theory

The notion of generalized group was introduced by Professor Molaei. After that he introduced top spaces as a generalization of Lie groups in 2004. A top space is a generalized group and a smooth manifold that its multiplication and inverse maps are smooth. In this book we give a review of recent works on top spaces with finite number of identities and a kind of top spaces with infinte number of identities (right top spaces).