Displaying similar documents to “Classification of obstructions for separation of semialgebraic sets in dimension 3.”

On certain compact topological spaces.

Manuel Valdivia (1997)

Revista Matemática de la Universidad Complutense de Madrid

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A compact topological space K is in the class A if it is homeomorphic to a subspace H of [0,1]I, for some set of indexes I, such that, if L is the subset of H consisting of all {xi : i C I} with xi=0 except for a countable number of i's, then L is dense in H. In this paper we show that the class A of compact spaces is not stable under continuous maps. This solves a problem posed by Deville, Godefroy and Zizler.

A really elementary proof of real Lüroth's theorem.

T. Recio, J. R. Sendra (1997)

Revista Matemática de la Universidad Complutense de Madrid

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Classical Lüroth theorem states that every subfield K of K(t), where t is a transcendental element over K, such that K strictly contains K, must be K = K(h(t)), for some non constant element h(t) in K(t). Therefore, K is K-isomorphic to K(t). This result can be proved with elementary algebraic techniques, and therefore it is usually included in basic courses on field theory or algebraic curves. In this paper we study the validity of this result under weaker assumptions: namely, if K...

A note on a theorem of Horikawa.

Francesco Zucconi (1997)

Revista Matemática de la Universidad Complutense de Madrid

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In this paper we classify the algebraic surfaces on C with KS2=4, pg=3 and canonical map of degree d=3. By our result and the previous one of Horikawa (1979) we obtain the complete determination of surfaces with K2=4 and pg=3.

Yamada polynomial and crossing number of spatial graphs.

Tomoe Motohashi, Yoshiyuki Ohyama, Kouki Taniyama (1994)

Revista Matemática de la Universidad Complutense de Madrid

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In this paper we estimate the crossing number of a flat vertex graph in 3-space in terms of the reduced degree of its Yamada polynomial.

Levelled O-minimal structures.

David Marker, Chris Miller (1997)

Revista Matemática de la Universidad Complutense de Madrid

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We introduce the notion of leveled structure and show that every structure elementarily equivalent to the real expo field expanded by all restricted analytic functions is leveled.