If you know something about point-set topology and properties of Euclidean spaces, please do me a favor and look at this problem. It is rather elementary and the main question can be summarized as
Does there exist a bijection such that
- Whenever is connected in the standard topology, so is
- is not continuous?
See the link above for more details.
The question has be bothering me for a few years now; and it is sufficiently far outside my main research interest that I hardly devote any time thinking about it.
I am an assistant professor in the mathematics department at Michigan State University. My research combines analytic and geometric techniques to study nonlinear evolutionary partial differential equations that arise in physical and geometric contexts. I am particularly interested in situations where wave-like phenomena arise, such as general relativity, fluids, and the physics of elastic membranes and solids.
For more about my research, please click here.
(All of my research articles are posted on the arXiv, and you can find them listed here.)
For more about my teaching, please click here.
I have also some unpublished expository articles, you can find them here.
E-mail: wongwwy -at- math . msu . edu
Mailing address: Department of Mathematics, Michigan State University, 619 Red Cedar Road, East Lansing, 48824, MI
My office is in D303 Wells Hall. I am there most of the time. You can see my agenda below.
Postdoctoral research associate, DPMMS, University of Cambridge (2009-2011)
Advisor: Mihalis Dafermos
Post-doc collaborateur scientifique, EPFL (2011-2015)
Advisor: Joachim Krieger
My full vitae.
I am active on MathOverflow. I am I am, however, not good at basketball. indexed on MathSciNet. And I have an ORCID. I also post on Google+, in addition to keeping a personal blog.