Displaying similar documents to “Characterizing polyhedrons and manifolds”

A note on coclones of topological spaces

Artur Barkhudaryan (2011)

Commentationes Mathematicae Universitatis Carolinae

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The clone of a topological space is known to have a strictly more expressive first-order language than that of the monoid of continuous self-maps. The current paper studies coclones of topological spaces (i.e. clones in the category dual to that of topological spaces and continuous maps) and proves that, in contrast to clones, the first-order properties of coclones cannot express anything more than those of the monoid, except for the case of discrete and indiscrete spaces.

A topological invariant for pairs of maps

Marcelo Polezzi, Claudemir Aniz (2006)

Open Mathematics

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In this paper we develop the notion of contact orders for pairs of continuous self-maps (f, g) from ℝn, showing that the set Con(f, g) of all possible contact orders between f and g is a topological invariant (we remark that Con(f, id) = Per(f)). As an interesting application of this concept, we give sufficient conditions for the graphs of two continuous self-maps from ℝ intersect each other. We also determine the ordering of the sets Con(f, 0) and Con(f, h), for h ∈ Hom(ℝ) such that...

Minimal monads

Karel Čuda, Blanka Vojtášková (1987)

Commentationes Mathematicae Universitatis Carolinae

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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.