Continuum Theory Seminar

Ana Mamatelashvili: Strengthenings of arc-connectedness

Abstract: A space is said to be n-arc connected if any n points are contained in an arc. I will show that a finite graph is 7-arc connected if and only if it is n-arc connected for every n if and only it is one of the six graphs that we can list out. If there is time I will also consider a further strengthening of this property, namely, requiring any countable set of points to be contained in an arc, and prove that there are only finitely many continua that satisfy this property.