To reference in my thesis, at first, I'd like a book of general topology that addressed convergence of sequences in topological spaces not necessarily metrizables. The concept seems plausible in Hausdorff topological spaces. See these notes for more.
The references I could get (as the books of John L. Kelley, MG Murdeshwar and Bourbaki) do not address sequences in topological spaces. In fact, Kelley's book is a brief definition of sequences in first countable topological spaces. But its definition depends completely on the definition of convergence in nets. And I do not want to deal with convergence in nets.
Question: Is there a book of general topology well accepted by the mathematical community to define convergence in topological spaces without speaking nets?
Question: Is there any research article that talks about convergence of sequences in topological spaces?