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Accessible points of arc-like continua

Andrea Ammerlaan ⟨ajammerlaan879@my.nipissingu.ca⟩

Abstract:

This talk will discuss the Nadler-Quinn problem. Posed in 1972, the problem asks if, given any arc-like continuum $X$ and any point $x \in X$, we can embed $X$ in the plane with $x$ accessible. In 2001, Minc constructed a particularly simple example of an arc-like continuum $X$ and point $p \in X$ for which it was not known whether $p$ could be made accessible in a plane embedding of $X$. In 2020, Anusic proved that $X$ can, in fact, be embedded with $p$ accessible. I will give an overview of this proof and briefly introduce a more recent approach to the problem.

Status: Accepted

Collection: Continuum Theory

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