Abstract p]As mentioned in the introduction, we shall present the theory of Borel sets in the general context of Polish spaces. In this chapter we give an account of Polish spaces. The space ℕℕ of sequences of natural numbers, equipped with the product of discrete topologies on ℕ, is of particular importance to us. Our theory takes a particularly simple form on this space, and it is possible to generalize the results on Borel subsets of ℕℕ to general Polish spaces. The relevant results that we shall use to obtain these generalizations are presented in the last section of this chapter.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
Rights and permissions
Copyright information
© 1998 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
(1998). Topological Preliminaries. In: A Course on Borel Sets. Graduate Texts in Mathematics, vol 180. Springer, New York, NY. https://doi.org/10.1007/978-0-387-22767-2_2
Download citation
DOI: https://doi.org/10.1007/978-0-387-22767-2_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98412-4
Online ISBN: 978-0-387-22767-2
eBook Packages: Springer Book Archive