Welcome to the InfoSci Platform
Different Types of Compactness and Their Importance in Causality

Different Types of Compactness and Their Importance in Causality

Dwaipayan Mishra, Himadri Shekhar Mondal
Copyright: © 2023 |Pages: 18
ISBN13: 9781668473436|ISBN10: 1668473437|ISBN13 Softcover: 9781668473443|EISBN13: 9781668473450
DOI: 10.4018/978-1-6684-7343-6.ch013
Cite Chapter Cite Chapter

MLA

Mishra, Dwaipayan, and Himadri Shekhar Mondal. "Different Types of Compactness and Their Importance in Causality." Constraint Decision-Making Systems in Engineering, edited by Santosh Kumar Das and Nilanjan Dey, IGI Global, 2023, pp. 239-256. https://doi.org/10.4018/978-1-6684-7343-6.ch013

APA

Mishra, D. & Mondal, H. S. (2023). Different Types of Compactness and Their Importance in Causality. In S. Das & N. Dey (Eds.), Constraint Decision-Making Systems in Engineering (pp. 239-256). IGI Global. https://doi.org/10.4018/978-1-6684-7343-6.ch013

Chicago

Mishra, Dwaipayan, and Himadri Shekhar Mondal. "Different Types of Compactness and Their Importance in Causality." In Constraint Decision-Making Systems in Engineering, edited by Santosh Kumar Das and Nilanjan Dey, 239-256. Hershey, PA: IGI Global, 2023. https://doi.org/10.4018/978-1-6684-7343-6.ch013

Export Reference

Mendeley
Favorite

Abstract

The notions of different types of compactness in a spacetime manifold has reviewed in this article. Also, their relations with Cauchy hypersurfaces, which play very important role in globally hyperbolic spacetimes has been discussed. For example, A be a closed subset of a spacetime M having a compact intersection with all the Cauchy hypersurfaces of it, then A⊂J(C) for some compact set C⊂M and conversely. Past and future compact sets in a spacetime and their interrelations with spacelike and timelike compactness are also discussed here by introducing necessary definitions, propositions, and diagrams wherever necessary, for the sake of understanding. Also, it is shown that, a closed advanced set is strictly future compact set. The relations among those compact sets themselves has been mentioned elaborately.

Request Access

You do not own this content. Please login to recommend this title to your institution's librarian or purchase it from the IGI Global bookstore.