Displaying similar documents to “Ultrametrics and infinite dimensional whitehead theorems in shape theory.”

Function spaces and shape theories

Jerzy Dydak, Sławomir Nowak (2002)

Fundamenta Mathematicae

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The purpose of this paper is to provide a geometric explanation of strong shape theory and to give a fairly simple way of introducing the strong shape category formally. Generally speaking, it is useful to introduce a shape theory as a localization at some class of “equivalences”. We follow this principle and we extend the standard shape category Sh(HoTop) to Sh(pro-HoTop) by localizing pro-HoTop at shape equivalences. Similarly, we extend the strong shape category of Edwards-Hastings...

Shape Correspondence Analysis for Biomolecules Based on Volumetric Eigenfunctions

Tao Liao, Hao-Chih Lee, Ge Yang, Yongjie Jessica Zhang (2015)

Molecular Based Mathematical Biology

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The functionality of biomolecules depends on their flexible structures, which can be characterized by their surface shapes. Tracking the deformation and comparing biomolecular shapes are essential in understanding their mechanisms. In this paper, a new spectral shape correspondence analysis method is introduced for biomolecules based on volumetric eigenfunctions. The eigenfunctions are computed from the joint graph of two given shapes, avoiding the sign flipping and confusion in the...

Shape index in metric spaces

Francisco R. Ruiz del Portal, José M. Salazar (2003)

Fundamenta Mathematicae

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We extend the shape index, introduced by Robbin and Salamon and Mrozek, to locally defined maps in metric spaces. We show that this index is additive. Thus our construction answers in the affirmative two questions posed by Mrozek in [12]. We also prove that the shape index cannot be arbitrarily complicated: the shapes of q-adic solenoids appear as shape indices in natural modifications of Smale's horseshoes but there is not any compact isolated invariant set for any locally defined map...