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Displaying similar documents to “Topological transitivity and strong transitivity.”

The Riemann theorem and divergent permutations

Roman Wituła (1996)

Colloquium Mathematicae

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In this paper the fundamental algebraic propeties of convergent and divergent permutations of ℕ are presented. A permutation p of ℕ is said to be divergent if at least one conditionally convergent series ∑ a n of real terms is rearranged by p to a divergent series ∑ a p ( n ) . All other permutations of ℕ are called convergent. Some generalizations of the Riemann theorem about the set of limit points of the partial sums of rearrangements of a given conditionally convergent series are also studied. ...

A descriptive, additive modification of Mawhin's integral and the Divergence Theorem with singularities

Dirk Jens F. Nonnenmacher (1994)

Annales Polonici Mathematici

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Modifying Mawhin's definition of the GP-integral we define a well-behaved integral over n-dimensional compact intervals. While its starting definition is of Riemann type, we also establish an equivalent descriptive definition involving characteristic null conditions. This characterization is then used to obtain a quite general form of the divergence theorem.

Commuting functions and simultaneous Abel equations

W. Jarczyk, K. Łoskot, M. C. Zdun (1994)

Annales Polonici Mathematici

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The system of Abel equations α(ft(x)) = α(x) + λ(t), t ∈ T, is studied under the general assumption that f t are pairwise commuting homeomorphisms of a real interval and have no fixed points (T is an arbitrary non-empty set). A result concerning embeddability of rational iteration groups in continuous groups is proved as a simple consequence of the obtained theorems.

Tietze Extension Theorem for n-dimensional Spaces

Karol Pąk (2014)

Formalized Mathematics

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In this article we prove the Tietze extension theorem for an arbitrary convex compact subset of εn with a non-empty interior. This theorem states that, if T is a normal topological space, X is a closed subset of T, and A is a convex compact subset of εn with a non-empty interior, then a continuous function f : X → A can be extended to a continuous function g : T → εn. Additionally we show that a subset A is replaceable by an arbitrary subset of a topological space that is homeomorphic...