Abstract

In this paper, we define a berbering of a Peano continuum, which is the space one gets by attaching a null sequence of circles to a countable dense subset of a Peano continuum. The topology of a berbering is one that recognizes which circles are small, in the sense that any neighborhood of the original Peano continuum will entirely contain all but finitely many of the attached circles. We then show that given a berbering of any simply connected, locally simply connected Peano continuum $Y$, there exists a one-dimensional Peano continuum $X$ and a map from $X$ to the berbering of $Y$ that induces a surjective homomorphism on their fundamental groups.

Degree

College and Department

Computational, Mathematical, and Physical Sciences; Mathematics

Rights

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