Abstract
The chapter begins with a fuller discussion of sets and functions, and includes the constructive meaning of such terms as subset, union, and inclusion. Certain classical laws of the algebra of sets carry over, and others do not. In Section 2 we introduce the basic notion of a complemented set, which is used in Chapter6 to facilitate the development of the theory of measure and integration. The chapter closes with some remarks on general topology which support the conclusion that in most cases of interest it is inappropriate to define continuous functions in terms of the family of open sets.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bishop, E., Bridges, D. (1985). Set Theory. In: Constructive Analysis. Grundlehren der mathematischen Wissenschaften, vol 279. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61667-9_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-61667-9_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64905-9
Online ISBN: 978-3-642-61667-9
eBook Packages: Springer Book Archive