Zoom link: https://pitt.zoom.us/j/93057796857
meeting id 930 5779 6857)
Abstract or Additional Information
This is a joint work with Evgenii Reznichenko.
A topological group G is said to be R-factorizable if, given any continuous function f : G → R, there exists a continuous homomorphism h: G → H to a second-countable topological group H and a continuous function g : H → R such that f = g ◦ h. The main unsolved problems of the theory of R-factorizable groups are as follows:
1. Is any R-factorizable group pseudo-א1-compact? (A space is pseudo-א1-compact if it contains no uncountable locally finite family of open sets.)
2. Is the image of an R-factorizable group under a continuous homomorphism R-factorizable?
3. Is the property of being an R-factorizable group topological? In other words, is any topological group homeomorphic to an R-factorizable one R-factorizable?
4. Is the square of an R-factorizable group R-factorizable?
Among other results we show that if the answer to question 1 is negative, then so are the answers to questions 2 and 4. Also, if the answer to question 4 is positive, then so are the answers to questions 2 and 3.