Displaying similar documents to “A Salamander Sculpture Barn Raising”

Finite-to-one maps and dimension

Jerzy Krzempek (2004)

Fundamenta Mathematicae

Similarity:

It is shown that for every at most k-to-one closed continuous map f from a non-empty n-dimensional metric space X, there exists a closed continuous map g from a zero-dimensional metric space onto X such that the composition f∘g is an at most (n+k)-to-one map. This implies that f is a composition of n+k-1 simple ( = at most two-to-one) closed continuous maps. Stronger conclusions are obtained for maps from Anderson-Choquet spaces and ones that satisfy W. Hurewicz's condition (α). The...

Algebraic theory of fundamental dimension

Sławomir Nowak

Similarity:

CONTENTSIntroduction......................................................................................................................................... 5Chapter I Elementary topological characterizations of fundamental dimension........................... 6 1. Characterizations of fundamental dimension..................................................................... 6 2. The fundamental dimension of components of compacta.............................................. 9 3. The...

On conjugacy equation in dimension one

Krzysztof Ciepliński, Zbigniew Leśniak (2013)

Banach Center Publications

Similarity:

In this paper, recent results on the existence and uniqueness of (continuous and homeomorphic) solutions φ of the equation φ ∘ f = g ∘ φ (f and g are given self-maps of an interval or the circle) are surveyed. Some applications of these results as well as the outcomes concerning systems of such equations are also presented.

The topological fixed point property - an elementary continuum-theoretic approach

Roman Mańka (2007)

Banach Center Publications

Similarity:

A set contained in a topological space has the topological fixed point property if every continuous mapping of the set into itself leaves some point fixed. In 1969, R. H. Bing published his article The Elusive Fixed Point Property, posing twelve intriguing and difficult problems, which exerted a great influence on the study of the fixed point property. We now present a survey article intended for a broad audience that reports on this area of fixed point theory. The exposition is also...

Universal measure zero, large Hausdorff dimension, and nearly Lipschitz maps

Ondřej Zindulka (2012)

Fundamenta Mathematicae

Similarity:

We prove that each analytic set in ℝⁿ contains a universally null set of the same Hausdorff dimension and that each metric space contains a universally null set of Hausdorff dimension no less than the topological dimension of the space. Similar results also hold for universally meager sets. An essential part of the construction involves an analysis of Lipschitz-like mappings of separable metric spaces onto Cantor cubes and self-similar sets.