Open locally semi-algebraic maps

Semi-θ-Open Sets and New Classes of Maps

semi-θ-open sets and new classes of maps

Semi-algebraic neighborhoods of closed semi-algebraic sets

— Given a closed (not necessarly compact) semi-algebraic set X in Rn, we construct a non-negative semi-algebraic C2 function f such that X=f−1(0) and such that for δ > 0 sufficiently small, the inclusion of X in f−1([0, δ]) is a retraction. As a corollary, we obtain several formulas for the Euler characteristic of X. Résumé. — Étant donné un ensemble semi-algébrique fermé (non nécessairement co...

Algebraic Formalism over Maps

This paper describes features of a language approach for map algebra based on the use of algebraic expressions. To be consistent with formal approaches such as geoalgebra and image algebra, the proposed algebraic expressions are suitable for the usual modeling of layers and to represent neighborhoods and zones. A tight compromise between language and implementation issues based on the theory of...

Entropy of algebraic maps

In this paper I give upper bounds for the entropy of algebraic maps in terms of certain homological data induced by their graphs. AMS classification 28D20, 30D05, 54H20 §0. Introduction Let X be a compact metric space and Γ ⊂ X ×X be a closed set. Set