topological
Continuous deformation study
Topological describes properties that remain unchanged when a shape is stretched, bent, or twisted—but not torn or glued.
In topology, a coffee mug and a doughnut are equivalent because each has exactly one hole.
The term extends to any analysis concerned with spatial relationships and connectivity rather than precise measurements: a topological map of the subway system.
Tied rope fastening
- torusDoughnut-shaped solid
- MöbiusTwisted loop topology
- surfaceOutermost boundary layer
- genusTaxonomic rank above species
orientable · sphere · handle · triangulation · tessellation · polyhedron · vertex · edge
Not closed
- closedNot accessible now
- neighborhoodResidential area nearby
- boundaryLine marking a limit
- convergenceProcess of approaching sameness
metric · compact · connected · separable · locally · subspace · cover · uniformity
Structural similarity through descent
- manifoldMany and various
- EulerProlific 18th-century mathematician
- connectednessState of being linked
- compactnessState of being compressed
genus · category · algebraic · invariant · embedding · immersion
Interconnected system
- connectivityState of being linked
- adjacencyState of being beside
- graphVisual data display
- nodeConnection point in networks
routing · GIS · overlay · proximity · containment · intersection · configuration · arrangement
Extending muscles or material
- bendingCurving from straight
- twistingRotating with distortion
- invariantRemaining always constant
- equivalenceState of being equal
preserving · distortion · morphing · transformation · contractible · retract
knot
Tied rope fastening
genus · orientable · sphere · handle · triangulation · tessellation · polyhedron · vertex · edge · face
open
Not closed
- closedNot accessible now
- neighborhoodResidential area nearby
- boundaryLine marking a limit
convergence · metric · compact · connected · separable · locally · subspace · cover · uniformity · interior
homology
Structural similarity through descent
- manifoldMany and various
- EulerProlific 18th-century mathematician
- connectednessState of being linked
compactness · genus · category · algebraic · invariant · embedding · immersion
network
Interconnected system
- connectivityState of being linked
- adjacencyState of being beside
- graphVisual data display
node · routing · GIS · overlay · proximity · containment · intersection · configuration · arrangement · relational
stretching
Extending muscles or material
equivalence · preserving · distortion · morphing · transformation · contractible · retract