the question is the type of algebraic object dexters represent. i’d like to believe they represent manifolds
linedexter
planedexter
spheredexter
torudexter
projectodexter
grassmanidexter
reimannidexter
etc.
i’d believe u though if u said that dexters must only be homotopically equivalent to a point or like have the same cohomology groups or wtv. balldexter. diskdexter.
Conjecture: Every beanisdexter is locally metrizable.
Proof is left as an important exercise for the reader.