Abstract
The set of rational numbers is ℚ. If A and B are subsets of ℝ then A + B = {x : x = a + b, a ∈ A, b ∈ B}. Similar conventions apply to AB and in general to “products” of subsets of algebraic structures. The set of complex numbers is ℂ and 𝕋 = {z: z ∈ ℂ, |z| = 1}; the latter is regarded as a group under ordinary multiplication. The set of Borel sets of ℝ is σR(O(ℝ)) (see Problem 4).
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
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1982 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Gelbaum, B.R. (1982). Topology. In: Problems in Analysis. Problem Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-7679-2_2
Download citation
DOI: https://doi.org/10.1007/978-1-4615-7679-2_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4615-7681-5
Online ISBN: 978-1-4615-7679-2
eBook Packages: Springer Book Archive