New Concepts of MetaStructures: Algebra, Topology, Lattices, Queues,
Markov Chains, and Intervals
Takaaki Fujita1,∗, Ajoy Kanti Das2
1Independent Researcher, Tokyo, Japan
2Associate Professor, Department of Mathematics, Tripura University, Agartala-799022, Tripura, India
Emails: Takaaki.fujita060@gmail.com; ajoykantidas@gmail.com
Abstract
A MetaStructure is a higher-level framework that treats entire collections of structures as single objects,
equipped with natural operations that preserve isomorphisms across different domains. The term “Struc-
ture” here refers broadly to mathematical systems as well as real-world models. An Iterated MetaStructure
generalizes this idea recursively, generating successive layers in which structures of structures form deeper
hierarchical meta-levels. In this work, we extend and investigate the properties of Algebra, Topology, Lattices,
Queues, Markov Chains, and Intervals through the lens of MetaStructures and Iterated MetaStructures.
Keywords: MetaStructure; Iterated MetaStructure; Algebra; Topology, Lattices; Queues; Markov Chains;
Interval