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A homological selection theorem implying a division theorem for Q-manifolds

Taras Banakh, Robert Cauty (2007)

Banach Center Publications

We prove that a space M with Disjoint Disk Property is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. This implies that the product M × I² of a space M with the disk is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. The proof of these theorems exploits the homological characterization of Q-manifolds due to Daverman and Walsh, combined with the existence of G-stable points in C-spaces. To establish the existence of such points we prove (and afterward...

Detecting codimension one manifold factors with the piecewise disjoint arc-disk property and related properties

Denise Halverson, Dušan Repovš (2013)

Open Mathematics

We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note that in every example presently known to the authors of a codimension one manifold factor of dimension n ≥ 4 determined by general position properties, the piecewise disjoint arc-disk...

Observability of control systems for polynomial inputs and genericity

Philippe Jouan (2001)

Applicationes Mathematicae

We consider smooth single-input, two-output systems on a compact manifold X. We show that the set of systems that are observable for any polynomial input whose degree is less than or equal to a given bound contains an open and dense subset of the set of smooth systems.

On manifolds with nonhomogeneous factors

Manuel Cárdenas, Francisco Lasheras, Antonio Quintero, Dušan Repovš (2012)

Open Mathematics

We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general topology concerning homogeneous spaces.

Singularité générique des applications différentiables de la 2-sphère dans une 3-variété différentiable

Jean-Loïc Batude (1971)

Annales de l'institut Fourier

Dans cet article nous étudions les singularités des applications différentiables de la deux sphère dans une trois variété avec les méthodes de transversalité et nous utilisons les résultats obtenus pour reprendre dans le cas différentiable, les démonstrations de Papakyriakopoulos et de Whitehead du théorème de la sphère.

The cell-like approximation theorem in dimension 5

Robert J. Daverman, Denise M. Halverson (2007)

Fundamenta Mathematicae

The cell-like approximation theorem of R. D. Edwards characterizes the n-manifolds precisely as the resolvable ENR homology n-manifolds with the disjoint disks property for 5 ≤ n < ∞. Since no proof for the n = 5 case has ever been published, we provide the missing details about the proof of the cell-like approximation theorem in dimension 5.

Tritangent planes to toroidal knots.

A. Montesinos Amilibia (1991)

Revista Matemática de la Universidad Complutense de Madrid

A proof is given that, with the only exception of (3,2), all toroidal knots in R3 obtained in the standard way by stereographic projection of knots in S3 have tritangent planes.

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