The main goal of this paper is to show that the inductive dimension of a
sigma-compact metric space X can be characterized in terms of
algebraical sums of connectivity (or Darboux) functions
X-->**R**.
As an intermediate step we show, using a result of Hayashi,
that for any dense G_{\delta} set G in
**R**^{2k+1} the union of G and some k homeomorphic images of G is
universal for k-dimensional separable metric spaces. We will also discuss
how our definition works with respect to other classes of Darboux-like
functions. In particular, we show that
for the class of peripherally continuous functions on an
arbitrary separable metric space X our parameter is equal to
either ind(X) or ind(X-1). Whether the later is at
all possible, is an open probem.

**Requires tcilatex.tex file**.
Uses amssym.cls.

**Last modified March 16, 2001.**