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Weakly Whitney preserving maps
Topology and its Applications, 2019For a metric continuum $X$, let $C(X)$ denote the hyperspace of subcontinua of $X$. For a map $f: X \rightarrow Y$ from a continuum $X$ to a continuum $Y$, let $\hat{f}$ denote the induced map (from $C(X)$ to $C(Y)$ given by $\hat{f}(A) = f(A)$ for all $A \in C(X)$).
Espinoza, Benjamin, Matsuhashi, Eiichi
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Canadian Mathematical Bulletin, 1980
In his recent book [3] Nadler observes that the property of admitting a Whitney map is of fundamental importance in studying the internal structure of hyperspaces, especially their arc structure. Nadler presents three distinct methods of constructing a Whitney map on the hyperspace 2X of nonempty closed subsets of a continuum.A partially ordered space ...
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In his recent book [3] Nadler observes that the property of admitting a Whitney map is of fundamental importance in studying the internal structure of hyperspaces, especially their arc structure. Nadler presents three distinct methods of constructing a Whitney map on the hyperspace 2X of nonempty closed subsets of a continuum.A partially ordered space ...
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Whitney Stratified Mapping Cylinders
Journal of Singularities, 2010In this paper we investigate (b)-regularity for stratied mapping cylinders CW0 (W ) of a stratied submersion f : W ! W 0 between two Whitney stratications. We show how Goresky's condition (D) for f is sucient to obtain ( b)-regularity of CW0 (W ). Revisiting some ideas of Goresky we give dierent proofs, a ner analysis and new equiv- alent properties.
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Whitney maps for spaces of embedding hypersurfaces
Mathematical Notes, 1992Let \(X\) be a metrizable compactum. The space \(\text{exp} X = \{A \subset X\) is nonempty and compact\} with Hausdorff metric is said to be the hyperspace \(\text{exp} X\) of a space \(X\) with metric \(\rho\). A closed subspace \({\mathcal A}\) of \(\text{exp} X\) is called an embedding hyperspace if for every \(A \in \text{exp} X\) such that \(A ...
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A note on generalized whitney maps
2015For metrizable continua, there exists the well-known notion of a Whitney map. Garcia-Velazquez extends the definition of Whitney map for C(X), where X is an arbitrary continuum (not necessarily metrizable). He also shows that the examples he considers do not admit such generalized Whitney maps.
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A Continuum X which has no Confluent Whitney Map for 2 x
Proceedings of the American Mathematical Society, 1984See the preview in Zbl 0524.54006.
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Tutte-Whitney Polynomials for Directed Graphs and Maps
2019Networks are used to model many real-world systems, including molecules, transportation systems, social networks, the World Wide Web and communication networks. Some applications require counting network substructures of many different types. The Tutte polynomial is a tool that is widely used for counting substructures in networks.
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Minimal Whitney stratification and Euler obstruction of discriminants
Geometriae Dedicata, 2016Gustavo Franco Barbosa, M J Saia
exaly