Fundamentos de Topologías de Vanguardia (artículo de revisión parcial)

Florentin Smarandache

Authors

Florentin Smarandache University of New Mexico, Mathematics, Physics and Natural Sciences Division

Keywords:

Classical Topology, Topological Space, NeutroSofication, AntiSofication, NeutroTopology, AntiTopology, Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, Super Hyper Hyper Topology, Neutro Super Hyper Topology, Extended Non-Standard Real Set, Non-Standard Topology, Non-Standard Neutrosophic Topology, Largest Extended Non-Standard Neutrosophic Topology; Left Monad, Right Monad, Perforated Binned, Left Closed Right Monad, Right Closed Left Monad, Non-Perforated Binned, Neutrosophic OverTopology, Neutrosophic InfraTopology, Neutrosophic ExtraTopology, (Fuzzy and Fuzzy-Extensions) Over/Infra/Extra-Topologies, Neutrosophic Multi-Set Topology

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.