FINAL STRUCTURED SUBSPACES

Abstract

Structured spaces or differential spaces are a generalization of the concept of smooth manifolds. Let (𝑀,𝜏,𝐶) be a structured space in the sense of Mostow and let 𝑓∶ (𝑀,𝜏,𝐶 ) → 𝑁 where 𝑁 is arbitrary, be a surjective function. There is a unique differential structure 𝐷 on 𝑁 determined by 𝑓 called the final, or identification differential structure, and the space 𝑁 then called the final structured space . In this paper, we will study structured subspaces of the final structured space (𝑁,𝐷). The case when the subspace of the space (𝑁,𝐷) is open is studied; and we prove that this subspace is also final. Some related concepts are defined and important properties are proved.KEYWORDS Diffeomorphism, Differential Structure, Smooth map, Final Structured Space, Structured Subspace.2010 Mathematics Subject Classification: 57R10, 58A40