Swiss cheeses

My readers may know that I do a lot of research on Swiss cheeses (though being mathematical, they tend to have infinitely many holes) [Note added: the Swiss cheeses, not the readers!].

 

CheeseColour

My latest joint paper on Swiss cheeses with my research students Sam Morley and Hongfei Yang, Abstract Swiss cheese space and classicalisation of Swiss cheeses , has just been published in Elsevier’s Journal of Mathematical Analysis and Applications. Thanks to funding from the EPSRC, this article has been made Open Access, so anyone can access the final published version free of charge at

http://dx.doi.org/10.1016/j.jmaa.2016.02.004

Of course much of the material is beyond the level of the typical undergraduate course. Nevertheless, students in 3rd/4th year might get something from looking at this. Abstract Swiss cheese space itself is really just a product of a sequence of standard spaces, but with elements interpreted as sequences of centres and radii of “abstract” discs. The two basic elementary geometric lemmas could probably be taught at GCSE!

 

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