topology
Geometry without distance
Topology is the branch of mathematics studying properties that remain unchanged when shapes are stretched, twisted, or deformed—but not torn or glued.
A coffee mug and a doughnut are topologically equivalent because each has one hole.
The word extends to any arrangement of interconnected elements: network topology, the topology of a computer system.
In anatomy, topology describes spatial relationships between body structures.
Many and various
- compactnessState of being compressed
- continuityUninterrupted progression or coherence
- boundaryLine marking a limit
- metricStandard of measurement
genus · torus · knot · orientable · neighborhood · connectedness · subspace
Bounding line of shape
- topographicalConcerning surface features
- surveySystematic data collection
- elevationHeight above reference point
- mapSpatial representation of terrain
relief · benchmark · datum · triangulation · USGS · ordinance · hillshade · isoline
Point where edges converge
- edgeBoundary or sharpness
- pathRoute for traveling
- cycleRepeating sequence of events
- nodeConnection point in networks
adjacency · degree · connected · planar · bipartite · spanning · tree · forest
Points of connection
- connectionsRelationships between things
- architectureBuilding design discipline
- meshInterlocking open weave
- starLuminous astronomical object
manifold
Many and various
- compactnessState of being compressed
- continuityUninterrupted progression or coherence
- boundaryLine marking a limit
metric · genus · torus · knot · orientable · neighborhood · connectedness · subspace
contour
Bounding line of shape
- topographicalConcerning surface features
- surveySystematic data collection
- elevationHeight above reference point
map · relief · benchmark · datum · triangulation · USGS · ordinance · hillshade · isoline · geospatial
vertex
Point where edges converge
node · adjacency · degree · connected · planar · bipartite · spanning · tree · forest · subgraph
nodes
Points of connection
- connectionsRelationships between things
- architectureBuilding design discipline
- meshInterlocking open weave
star · ring · bus · tree · hybrid · backbone · LAN · WAN · router · switch
elevation
Height above reference point
valley · ridge · plateau · canyon · watershed · drainage · slope · gradient · terrain · mountain
- 3D meshesvertex, edge, face, wireframe, connectivity
- Molecular Propertiesmolecular weight, molecular formula, solubility, polarity, hydrophobicity
- sciencesbiology, chemistry, physics, astronomy, geology
- disciplinesbiology, chemistry, physics, mathematics, psychology
- math conceptsangle, numbers, algebra, circle, equations
- college coursesbiology, calculus, chemistry, physics, quantum physics
topologyEuclidean geometry
Study of flat planes
metrology · mensuration · trigonometry · measurement · surveying