Subspace operations in affine Klingenberg spaces.

Bisztriczky, T.; Lorimer, J.W.

Displaying similar documents to “Subspace operations in affine Klingenberg spaces.”

On homeomorphic and diffeomorphic solutions of the Abel equation on the plane

Zbigniew Leśniak (1993)

Annales Polonici Mathematici

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We consider the Abel equation φ[f(x)] = φ(x) + a on the plane ℝ², where f is a free mapping (i.e. f is an orientation preserving homeomorphism of the plane onto itself with no fixed points). We find all its homeomorphic and diffeomorphic solutions φ having positive Jacobian. Moreover, we give some conditions which are equivalent to f being conjugate to a translation.

Addition of initial segments. II.

Antonín Sochor (1988)

Commentationes Mathematicae Universitatis Carolinae

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A dyadic view of rational convex sets

Gábor Czédli, Miklós Maróti, Anna B. Romanowska (2014)

Commentationes Mathematicae Universitatis Carolinae

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Let $F$ be a subfield of the field $ℝ$ of real numbers. Equipped with the binary arithmetic mean operation, each convex subset $C$ of $F^{n}$ becomes a commutative binary mode, also called idempotent commutative medial (or entropic) groupoid. Let $C$ and $C^{'}$ be convex subsets of $F^{n}$ . Assume that they are of the same dimension and at least one of them is bounded, or $F$ is the field of all rational numbers. We prove that the corresponding idempotent commutative medial groupoids are isomorphic iff the affine...