This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# Category:Topology

From Mathematics Is A Science

Jump to navigationJump to searchMost of the articles below have been significantly re-written and incorporated in the draft of a new book: Topology Illustrated.

## Subcategories

This category has the following 4 subcategories, out of 4 total.

## Pages in category "Topology"

The following 200 pages are in this category, out of 429 total.

(previous page) (next page)### A

- A Combinatorial Introduction to Topology by Henle
- A graph representation of the topology of color images by Saveliev
- A graph, non-tree representation of the topology of a gray scale image by Saveliev
- A Lefschetz-type coincidence theorem by Saveliev
- A new look at continuity
- Abstract simplicial complex
- Acyclic models
- Addition is continuous
- Advanced Topology -- Spring 2013
- Advanced Topology -- Spring 2013 -- final exam
- Advanced Topology: exercises
- Advanced Topology: midterm
- Alexander duality
- Algebraic topology and digital image analysis
- Algebraic topology: course
- Algorithm for binary images
- Algorithm for grayscale images
- Applications of Computational Topology by Christopher Johnson
- Applications of Lefschetz numbers in control theory by Saveliev
- Applied algebraic topology
- Applied Topology and Geometry
- Applied Topology and Geometry: preface
- Approximating paths
- Arc-length and curvature
- Are intervals homeomorphic?
- Axioms of calculus
- Axioms of chain complexes
- Ayasdi

### B

- Ball
- Banach fixed point theorem
- Barycentric subdivision
- Bases of neighborhoods
- Basic Topology by Armstrong
- Basis of topology
- Betti numbers
- Binary watershed
- Bordism
- Borsuk-Ulam theorem
- Boundaries in gray scale images
- Boundary
- Boundary group
- Boundary operator
- Boundary operator of simplicial complexes
- Brouwer fixed point theorem

### C

- Calculus / algebra = topology
- Calculus and algebra vs topology
- Calculus as a part of topology
- Calculus is the dual of topology
- Calculus on chains
- Calculus on cubical complexes
- Can a set to be both open and closed?
- Cap product
- Cell
- Cell complex
- Cell decomposition of images
- Cell maps
- Cells
- Cells and cell complexes
- Cellular automata
- Chain complex
- Chain complexes of cell complexes
- Chain operators
- Chains vs cochains
- CHomP
- CHomP examples
- Circle
- Classification of points with respect to a subset
- Classification of surfaces
- Closed curve
- Closedness and exactness of 1-forms
- Co-boundary operator
- Cochain complex
- Cochain complexes and cohomology
- Cochain operators
- Cochains on graphs
- Codifferential
- Codiffferential
- Cohomology
- Compact spaces
- Compact-open topology
- Compactness
- Compositions of simplicial maps
- Computational Homology by Kaczynski, Mischaikow, Mrozek
- Computational science training: 2010 projects
- Computational science training: 2011 projects
- Computational science training: 2012
- Computational topology
- Computational Topology by Edelsbrunner and Harer
- Computing homology
- Computing persistent homology of filtrations
- Cone
- Configuration spaces
- Connected sum
- Connectedness
- Connectivity
- Constant homotopy between constant maps
- Constant map
- Continuity as accuracy
- Continuity of functions of several variables
- Continuity under algebraic operations
- Continuous functions
- Continuous vs discrete differential forms
- Control
- Convergence
- Cube
- Cubical chain complex
- Cubical complex
- Cubical tangent bundle
- Cup product
- Current students' projects
- Curve
- Cycle
- Cycle group
- Cycles in images
- Cylinder

### D

- Data made Euclidean
- De Rham cohomology
- De Rham map
- Deformation retract
- Degree of map
- Diagonal map
- Differential forms and cohomology: course
- Differential Forms: A Complement to Vector Calculus by Weintraub
- Differential forms: course
- Differential forms: exams
- Differential forms: review questions
- Diffusion
- Diffusion with various geometry
- Digital curves
- Dilation and erosion
- Dimension
- Discrete calculus course
- Discrete Calculus. An Introduction
- Discrete Calculus: Applied Analysis on Graphs for Computational Science by Grady and Polimeni
- Discrete calculus: contributors
- Discrete differential geometry
- Discrete exterior calculus
- Discrete forms
- Discrete forms and cochains
- Discrete Hodge star operator
- Dual cells and dual forms

### E

- Edge detection
- Eilenberg–Steenrod axioms of homology
- Equilibria of dynamical systems
- Euclidean space
- Euclidean space made discrete
- Euler
- Euler and Lefschetz numbers
- Euler characteristic
- Euler characteristic of graphs
- Euler characteristic of surfaces
- Euler number of digital images
- Euler-Poincare formula
- Evaluating image-to-image search
- Exact sequences
- Examples of cell complexes
- Examples of homology of cubical complexes
- Examples of maps

### F

- Fiber bundle
- Filtration
- Fingerprint identification
- Fixed points
- Fixed Points and Coincidences by Saveliev
- Fixed points and selections of set valued maps on spaces with convexity by Saveliev
- Forms
- Forms in Euclidean spaces
- From Calculus to Cohomology by Madsen
- From continuity to point-set topology
- Functions of several variables: exercises
- Fundamental class
- Fundamental group

### G

### H

- Hausdorff distance
- Hausdorff space
- Hawaiian earring
- Higher order Nielsen numbers by Saveliev
- Hodge decomposition
- Hodge dual
- Hodge duality of cubical forms
- Hodge duality of differential forms
- Homeomorphism
- Homology
- Homology and algebra
- Homology and cohomology operators
- Homology as a group
- Homology as a vector space
- Homology as an equivalence relation
- Homology classes