topologically
In continuous deformation
Topologically describes something in terms of topology, the branch of mathematics concerned with properties that remain unchanged when shapes are stretched, twisted, or deformed without tearing or gluing.
A coffee mug and a doughnut are topologically equivalent because each has exactly one hole.
The adverb appears in technical contexts: The two surfaces are topologically identical.
Outside mathematics, it sometimes describes spatial relationships or connectedness in networks and systems.
Many and various
- compactnessState of being compressed
- connectednessState of being linked
- invariantRemaining always constant
- continuousWithout pause or gap
Euler · genus · isomorphism · neighborhood · basis · subspace · boundary · covering
Doughnut-shaped solid
- spherePerfectly round solid
- knotTied rope fastening
- surfaceOutermost boundary layer
- cylinderCircular-based solid form
projective plane · genus · planar · hyperbolic · Euclidean · non-Euclidean · polyhedron · tessellation
Ordered configuration or agreement
- configurationArrangement of parts
- layoutSpatial arrangement of elements
- structureArrangement of interconnected parts
- networkInterconnected system
adjacency · proximity · ordering · hierarchy · branching · clustering · connectivity · pathways
manifold
Many and various
- compactnessState of being compressed
- connectednessState of being linked
- invariantRemaining always constant
continuous · Euler · genus · isomorphism · neighborhood · basis · subspace · boundary · covering · orientable
torus
Doughnut-shaped solid
cylinder · projective plane · genus · planar · hyperbolic · Euclidean · non-Euclidean · polyhedron · tessellation · symmetry
arrangement
Ordered configuration or agreement
- configurationArrangement of parts
- layoutSpatial arrangement of elements
- structureArrangement of interconnected parts
network · adjacency · proximity · ordering · hierarchy · branching · clustering · connectivity · pathways · regions
stretch
Pull to extend
warp · fold · compress · expand · contract · rubber sheet · morph · reshape · equivalence · preserve
topologicallymetrically
In measured verse
isometrically · geometrically · numerically · quantitatively · analytically
topologicallyquantitatively
In numerical terms
numerically · computationally · arithmetically · statistically · measurably