4,615 research outputs found
On the one dimensional polynomial and regular images of
In this work we present a full geometric characterization of the
1-dimensional polynomial and regular images of and we compute for
all of them the invariants and , already introduced in
\cite{fg2}
On the complements of 3-dimensional convex polyhedra as polynomial images of
We prove that the complement of a 3-dimensional convex polyhedron and
its closure are polynomial images of .
The former techniques cannot be extended in general to represent such
semialgebraic sets and as polynomial
images of if .Comment: 12 pages, 1 figur
On spectral types of semialgebraic sets
In this work we prove that a semialgebraic set is
determined (up to a semialgebraic homeomorphism) by its ring
of (continuous) semialgebraic functions while its ring of
(continuous) bounded semialgebraic functions only determines besides a
distinguished finite subset . In addition it holds that the
rings and are isomorphic if and only if
is compact. On the other hand, their respective maximal spectra
and endowed with the Zariski topology are always homeomorphic and
topologically classify a `large piece' of . The proof of this fact requires
a careful analysis of the points of the remainder associated with formal paths.Comment: 22 page
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