  A visceral structure on M is given by a definable base for a uniform topology
on its universe in which all basic open sets are infinite and any infinite
definable subset X of M has non-empty interior. This context includes o-minimal
ordered groups, p-adic fields, and other examples.
  Assuming only viscerality, we show that the definable sets in M satisfy some
desirable topological tameness conditions. For example, any definable unary
function on M has a finite set of discontinuities; any definable function on a
Cartesian power of M is continuous on a nonempty open set; and assuming
definable finite choice, we obtain a cell decomposition result for definable
sets. Under an additional topological assumption ("no space-filling
functions"), we prove that the natural notion of topological dimension is
invariant under definable bijections. These results generalize theorems proved
by Simon and Walsberg, who assumed dp-minimality in addition to viscerality. In
the final section, we construct new examples of visceral structures.
