Fundamentals of Vanguard Topologies (partial review article)

Abstract

We have recently found nine new topologies: Non-Standard Topology, Further Extension of Real Non-Standard Topology, Weak/Strong Neutrosophic Triplet Topologies, Weak/Strong Neutrosophic Extended Triplet Topologies, Neutrosophic Dupla Topology, Neutrosophic Extended Dupla Topology, Neutrosophic Multi Set Topology, and we recall and improve the previously founded seven topologies in the years (2019-2023), viz: Non-Standard Neutrosophic Topology, Neutrosophic Topology, Anti Topology, Refined Neutrosophic Topology, Refined Neutrosophic Sharp Topology, Super Hyper Topology and Super Hyper Neutrosophic Topology. They are called state-of-the-art topologies because of their innovative shapes.