**Speaker:** Dr. Lynne Yengulalp from Wake Forest University (invited by Will Brian)

**Date and Time:** Friday, February 25, 2022, 11:00-12:00 in person. The talk will also be broadcast online via Zoom for those unable to attend in person. Please contact Will Brian to obtain the Zoom link.

**Title:** Completeness in topology

**Abstract:** A metric space is complete if every Cauchy sequence converges (to a point in the space). The real line is complete, but the open unit interval (which is topologically the same, i.e. homeomorphic to the real line) is not complete. In this talk, we will survey some *topological* notions of completeness. One strong notion of completeness is complete metrizability; a space X is completely metrizable if it is homeomorphic to a complete metric space. On the weaker end, a space is called Baire if the intersection of countably many dense open sets is dense. There is an interesting spectrum of topological properties in between. Such properties arise from generalizing convergence of sequences, from topological games, and from domain theory.