topologists
Continuous deformation experts
Topologists are mathematicians who study topology—the branch of mathematics concerned with properties of shapes that remain unchanged when stretched, twisted, or deformed without tearing.
A topologist famously cannot distinguish a coffee mug from a doughnut, since both have exactly one hole.
Topologists proved the conjecture in 2006.
State of being compressed
- connectednessState of being linked
- continuityUninterrupted progression or coherence
- genusTaxonomic rank above species
- dimensionMeasurable extent or scope
contractible · local · separability · completeness · boundedness · closure · density · regularity
Many and various
- torusDoughnut-shaped solid
- MöbiusTwisted loop topology
- spherePerfectly round solid
- surfaceOutermost boundary layer
knot · link · braid · polyhedron · suspension · projective plane · handle · foliation
Mutual continuous deformation relationship
- embeddingPlacing within surrounding mass
- immersionState of being submerged
- retractionFormal withdrawal of statement
- inclusionBeing made part
projection · degree · lift
Prolific 18th-century mathematician
Structural similarity through descent
- linking numberInteger measuring curve entanglement
- indexAlphabetical guide to contents
- signatureHandwritten name for verification
- torsionRotational strain force
compactness
State of being compressed
- connectednessState of being linked
- continuityUninterrupted progression or coherence
- genusTaxonomic rank above species
dimension · contractible · local · separability · completeness · boundedness · closure · density · regularity · normality
manifold
Many and various
surface · knot · link · braid · polyhedron · suspension · projective plane · handle · foliation · lamination
homotopy equivalence
Mutual continuous deformation relationship
- embeddingPlacing within surrounding mass
- immersionState of being submerged
- retractionFormal withdrawal of statement
inclusion · projection · degree · lift
Euler
Prolific 18th-century mathematician
homology
Structural similarity through descent
- linking numberInteger measuring curve entanglement
- indexAlphabetical guide to contents
- signatureHandwritten name for verification
excision
Cutting out of tissue
- ham sandwichPork slices in bread
topologistsgeometers
Those who study spatial properties
surveyors · cartographers · architects · civil engineers · navigators
topology, isotopic, topological, topologically, topologies, topologic