topologically
Adverb
Meaning
from the point of view of topology
Source: WordNetSynonyms
Phrases with the word
Examples
A C*-algebra is a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties: * A is a topologically closed set in the norm topology of operators.
Algebraic topology is the study of topologically invariant abstract algebra constructions on topological spaces.
A topological space is Hausdorff if and only if it is both preregular (i.e. topologically distinguishable points are separated by neighbourhoods) and Kolmogorov (i.e. distinct points are topologically distinguishable).
Because of this, they are not necessarily topologically equivalent to the sphere as Platonic solids are, and in particular the Euler relation : does not always hold.
Conversely, the Lindenstrauss–Tzafriri theorem asserts that if every closed subspace of a Banach space is complemented, then the Banach space is isomorphic (topologically) to a Hilbert space.
Every polygon is topologically self-dual (it has the same number of vertices as edges, and these are switched by duality), but will not in general be geometrically self-dual (up to rigid motion, for instance).