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Category:Topology
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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.
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- Homology classes under maps
- Homology group of filtration
- Homology groups of filtrations
- Homology groups of graphs
- Homology in Calculus
- Homology in dimension 1
- Homology in dimension 2
- Homology maps
- Homology of balls and spheres
- Homology of cell complexes: course
- Homology of cubical complexes
- Homology of filtrations
- Homology of homotopic maps
- Homology of images
- Homology of maps
- Homology of parametric images by Saveliev
- Homology of surfaces
- Homology operator
- Homology software
- Homotopy
- Homotopy and homotopy equivalence
- Homotopy as a perturbation
- Homotopy equivalence
- How do you count holes in a binary image?
- How to compute Betti numbers
- How to compute homology
I
- Identity map
- Image processing: course
- Image segmentation
- Images as functions of two variables
- Inclusion tree
- Integer-valued calculus
- Integration of differential forms of degree 2
- Intersection of a finite collection of open sets is open
- Intersection of any collection of closed sets is closed
- Introduction to Topology by Gamelin and Greene
- Introduction to Topology: Pure and Applied by Adams and Franzosa
- Introductory algebraic topology: review exercises
- Is a closed subset of a compact space always compact?
- Is a constant function always continuous?
- Is a restriction of a continuous function always continuous?
- Is an open interval homeomorphic to a closed one?
- Is every set either open or closed?
- Is Mobius strip homeomorphic to the cylinder?
- Is the identity function always continuous?
- Is the image of a closed set under a contiuous function closed?
- Is the image of an open set under a continuous function open?
- Is the inclusion always continuous?
- Is the intersection of any collection of open sets always open?
- Is the inverse of a continuous function always continuous?
- Is the max of two continuous functions continuous?
- Is the union of any collection of closed sets always closed?
- Isotropy in numerical PDEs
L
- Labeling
- Lefschetz coincidence theory for maps between spaces of different dimensions by Saveliev
- Lefschetz number
- Lefschetz numbers in control theory
- Lefschetz theory for coincidences
- Limit of function
- Locally homeomorphic spaces
- Lomonosov's invariant subspace theorem for multivalued linear operators by Saveliev
M
- Manifolds
- Manifolds model a curved universe
- Map
- Maps of graphs
- Maps of polyhedra
- Mathematics of computer vision: course
- Mesh
- Metric
- Metric space
- Metric tensor
- Metric tensor in dimensions 1 and 2
- Mobius band
- More about manifolds
- Motion planning in robotics
- Multilinear algebra
- Multiparameter filtrations
N
O
P
- Parametric complexes
- Parametrized complexes
- Path
- Path-connectedness
- PDEs
- Persistence
- Persistence of homology classes in filtrations
- Persistence via homology operators
- Persistent Betti numbers
- Persistent homology
- Persistent homology groups of filtrations
- Physics
- Pixel
- Poincare duality
- Poincare-Hopf index theorem
- Point cloud
- Point-set topology: course
- Point-set topology: exercises
- Polyhedron
- Preface
- Primal and dual complexes
- Product topology
- Products
- Projection map
- Projective plane
- Properties of homology groups
- Prove that the composition of continuous functions is continuous
- Prove that two closed intervals are homeomorphic
R
- Realizations of cubical complexes
- Relative homology
- Relative topology
- Removing coincidences of maps between manifolds of different dimensions by Saveliev
- Retraction
- Robustness of topology
- Robustness of topology of digital images and point clouds by Saveliev
- Robustness of topology: persistence
- Rotation group
S
- Second derivative and the Laplacian
- Selection votes
- Separation axioms
- Set-valued maps
- Seurat's painting
- Short overview
- Simple curve
- Simplex
- Simplicial complexes
- Simplicial homology
- Simplicial maps
- Simplicial maps and chain maps
- Simply connected spaces
- Singular chain complexes
- Skeleton
- Social choice
- Sphere
- Spreadsheets
- Stages of analysis
- Subcomplexes
- Surface
- Surfaces and their homology
- Suspension
T
- Tame function
- Test
- The algebra of cells
- The algebra of chains
- The algebra of oriented cells
- The geometry a gray scale image
- The high contrast homology of a gray scale image
- The homology of a gray scale image
- The political spectrum is a circle
- The topology of a binary image
- The topology of a color image
- The topology of a gray scale image
- The topology of data
- Topography
- Topological circle
- Topological data analysis
- Topological equivalence
- Topological event
- Topological features of images
- Topological invariants
- Topological spaces
- Topologically closed
- Topology
- Topology 1: course
- Topology 2: course
- Topology based method of partition, analysis, and simplification of dynamical images: patent
- Topology based method of segmentation of gray scale images by Saveliev
- Topology for Computing by Zomorodian
- Topology graph
- Topology I -- Fall 2013
- Topology I -- Fall 2013 -- final exam
- Topology I -- Fall 2013 -- midterm
- Topology II -- final exam
- Topology II -- midterm
- Topology II -- Spring 2012
- Topology II -- Spring 2014
- Topology II -- Spring 2014 -- final exam
- Topology II -- Spring 2014 -- midterm