letxbe the set of real numbers and for each irrationalxwe choose a sequence {x$\displaystyle i$} of rationals converging to it in the euclidean topology .the rational sequence topology is the defined by declaring each rational open, and selecting the sets U$\displaystyle n$(x)={x$\displaystyle i$}(n from 0 to infinity) U {x} as a basis for the irrational point x.

can anyone tell me the following properties regarding the above topological space?

- basis

-sub basis

-interior and closure

-Both Open and Closed Sets

-Hausdorff Space and Metrizable Topology

-Relative Topology

-Finer and Coarser Topology

-Homeomorphism

-Connectedness

-Compactness

-Countability