In this paper, we introduced an equivalence between weak convergence of
filters and weak convergence of nets and show that, in Uryson spaces, as was done for
filters in [1], weak limits of nets are unique. Moreover, we show that, in a regular space
X, with E ⊆ X , x∈ E if and only if there is a net in X which converges weakly to x .
We also prove that closure continuous maps preserve weak convergence of nets. As a
main result, we prove that, in regular spaces, weak convergence of nets is equivalent to
their usual convergence, once again, a mimic of filters in [1]. 

Title

Annals of Pure and Applied Mathematics

Publisher

House of Scientific Research

Publisher Country

India

Publication Type

Prtinted only

Volume

5

Year

2017

Pages

525-530