General Topology. By Jacques Dixmier. General Topology and Homotopy Theory. By I. M. James;Topology. By Klaus Jänich

1987 ◽  
Vol 94 (5) ◽  
pp. 475-479
Author(s):  
Robert F. Brown
Keyword(s):  
Homotopy Theory ◽  
General Topology

scholarly journals Geometric Modelling of the Thinning by Cell Complexes

2019 ◽  
Vol 8 (2) ◽  
pp. 38
Author(s):  
Atefeh Hasan-Zadeh
Keyword(s):  
Pattern Recognition ◽  
Homotopy Theory ◽  
General Topology ◽  
Geometric Modelling ◽  
Active Area ◽  
Primary Role ◽  
Cell Complexes ◽  
Amount Of Information ◽  
Thinning Algorithms ◽  
Fixed Structure

Motivation: Thinning is an extremely active area of research because of its primary role in reducing the amount of information that must be processed by algorithms for pattern recognition. Most thinning algorithms are supposed to be topology-preserving, although an accurate statement of what this means is usually left unanswered.Results: The objective of this article is the presentation of a general topology via the concepts of homotopy theory to preserve the thinning. The proposed method can be applied to any decomposition of non-structural cells of the object, given that the cells have a fixed structure.  

On equivariant disconnected rational homotopy theory

2010 ◽  
Vol 17 (2) ◽  
pp. 229-240
Author(s):  
Marek Golasiński
Keyword(s):  
Homotopy Theory ◽  
Weak Equivalence ◽  
Rational Homotopy Theory ◽  
Rational Homotopy ◽  
Hamiltonian Group ◽  
Simplicial Set ◽  
De Rham

Abstract An equivariant disconnected Sullivan–de Rham equivalence is developed using Kan's result on diagram categories. Given a finite Hamiltonian group G, let X be a G-simplicial set. It is shown that the associated system of algebras indexed by the category 𝒪(G) of a canonical orbit can be “approximated” (up to a weak equivalence) by such a system ℳ X with the properties required by nonequivariant minimal algebras.

scholarly journals A First Approximation to Homotopy Theory

1953 ◽  
Vol 39 (7) ◽  
pp. 655-660 ◽  
Author(s):  
E. H. Spanier ◽  
J. H. C. Whitehead
Keyword(s):  
Homotopy Theory ◽  
First Approximation
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