  If a continuous map f: X->Q is approximable arbitrary closely by embeddings
X->Q, can some embedding be taken onto f by a pseudo-isotopy? This question,
called Isotopic Realization Problem, was raised by Shchepin and Akhmet'ev. We
consider the case where X is a compact n-polyhedron, Q a PL m-manifold and show
that the answer is 'generally no' for (n,m)=(3,6); (1,3), and 'yes' when:
  1) m>2n, (n,m)\neq (1,3);
  2) 2m>3(n+1) and the set {(x,y)|f(x)=f(y)} has an equivariant (with respect
to the factor exchanging involution) mapping cylinder neighborhood in X\times
X;
  3) m>n+2 and f is the composition of a PL map and a TOP embedding.
  In doing this, we answer affirmatively (with a minor preservation) a question
of Kirby: does small smooth isotopy imply small smooth ambient isotopy in the
metastable range, verify a conjecture of Kearton-Lickorish: small PL
concordance implies small PL ambient isotopy in codimension \ge 3, and a
conjecture set of Repovs-Skopenkov.
