Tools

Arthur Knoebel ()

Chapter III in Sheaves of Algebras over Boolean Spaces, 2012, pp 55-77 from Springer

Abstract: Abstract This chapter provides more background material; its four sections present briefly what needs to be known about logic, category theory, point-set topology, and Boolean algebra. The first section reviews equational logic, model theory, and set theory. Terms and free algebras are built, and the basic properties of varieties are developed. The next section gives the notions needed from category theory, with few proofs. We head for adjunctions and equivalences between two categories. The third section sketches various kinds of topological spaces, including Boolean spaces, and new spaces are built out of old. Boolean algebras, in the last section, are important. They have a topological dual in Boolean spaces, created in two ways on prime ideals: the Stone topology through clopen sets, or equivalently the hull-kernel topology.

Keywords: Topological Space; Prime Ideal; Boolean Algebra; Integral Domain; Natural Transformation (search for similar items in EconPapers)
Date: 2012
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-4642-4_3

Ordering information: This item can be ordered from
http://www.springer.com/9780817646424

DOI: 10.1007/978-0-8176-4642-4_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().