  We are concerned with topology of Hensel minimal structures on non-trivially
valued fields $K$, whose axiomatic theory was introduced in a recent paper by
Cluckers-Halupczok-Rideau. We additionally require that the value group and
residue field are orthogonal and that the definable sets in the value group
sort are already definable in the language of ordered groups. This condition is
satisfied by several classical tame structures on Henselian fields, including
Henselian fields with analytic structure, V-minimal fields and polynomially
bounded o-minimal structures with a convex subring. In this article, we
establish many results concerning definable functions and sets. These are,
among others, existence of the limit for definable functions of one variable, a
closedness theorem, several non-Archimedean versions of the Lojasiewicz
inequalities, an embedding theorem for regular definable spaces, and the
definable ultranormality and ultraparacompactness of definable Hausdorff
LC-spaces.
