New Types of Topologies and Neutrosophic Topologies (Improved Version)

Abstract

In this paper we recall the six new types of topologies, and their corresponding
topological spaces, that we introduced in the last years (2019-20223), such as: NeutroTopology,
AntiTopology, Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology,
SuperHyperTopology, and Neutrosophic SuperHyperTopology.
The nth-PowerSets
( ) n P H
and
*
( ) n P H
, that the SuperHyperTopology and respectively
Neutrosophic SuperHyperTopology are based on, better describe our real world, since a system H
(that may be a set, company, institution, country, region, etc.) is organized in sub-systems, which in
their turn are organized each in sub-sub-systems, and so on