Title

Disjoint Infinity Borel Functions

Author(s)

Daniel Hathaway, University of DenverFollow

Document Type

Topology + Foundations

Publication Date

6-2017

Publication Source

32nd Summer Conference on Topology and Its Applications

Abstract

Consider the statement that every uncountable set of reals can be surjected onto R by a Borel function. This is implied by the statement that every uncountable set of reals has a perfect subset. It is also implied by a new statement D which we will discuss: for each real a there is a Borel function f_a : RtoR and for each function g : RtoR there is a countable set G(g) of reals such that the following is true: for each a in R and for each function g : R to R, if f_a is disjoint from g, then a is in G(g). We will show that D follows from ZF +AD⁺ whereas the negation of D follows from ZFC.

Comments

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Copyright

Copyright © 2017, the Author

eCommons Citation

Hathaway, Daniel, "Disjoint Infinity Borel Functions" (2017). Summer Conference on Topology and Its Applications. 10.
https://ecommons.udayton.edu/topology_conf/10