On the Upper Bound of the Cardinality of Topological Spaces

In the first part of this talk we will compare some known results about the upper bound of the cardinality of Hausdorff topological spaces and will mention some improvements of some of the most celebrated cardinal inequalities for Hausdorff topological spaces. In the second part of the talk, we will show how some of the previously mentioned cardinal inequalities  for Hausdorff topological spaces could be extended to be valid for all topological spaces.