On τ-base and e-density of topological spaces

In this paper, we prove some properties of families of ?-open sets, study the properties of the space of ?-continuous mappings, as well as the properties of the e-density of topological spaces. We prove an analogue of A.V.Arkhangelskii?s theorem for ?-base. Also we showed that the base of a topological space is not always a ?-base. We introduce the notion of e-density of topological spaces. As well as, we investigate some properties of this cardinal function. It is given an example of a topological space, e-density of which is not equal to its density.

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