How do you determine topologically equivalent?
How do you determine topologically equivalent?
An equivalence relation between topological spaces. Two topological spaces X and Y are said to be topologically equivalent (or homeomorphic), if there exists a homeomorphism, continuous map between the spaces, H∈C0(X,Y) which has a continuous inverse H−1∈C0(Y,X).
What is the meaning of topologically?
Definition of topological 1 : of or relating to topology. 2 : being or involving properties unaltered under a homeomorphism continuity and connectedness are topological properties.
What is topologically equivalent to a torus?
Polyhedra with the topological type of a torus are called toroidal polyhedra, and have Euler characteristic V − E + F = 0.
How do you prove two metrics are topologically equivalent?
We say that two metrics are equivalent if the two induced topologies are equal. Let d and d′ be two metrics on a set M. Then d and d′ are equivalent if and only if the following condition is satisfied: for every x∈M and every r>0 there exist r1,r2>0 such that B(d′)r1(x)⊆B(d)r(x) and B(d)r2(x)⊆B(d′)r(x).
What does topologically equivalent mean biology?
Molecules can get from one to another without having to cross a membrane. Spaces within the cell are considered topologically equivalent if molecules can move between them without crossing a membrane. Molecules use translocators to get from one to the other.
Is a sphere topologically equivalent to a circle?
A circle is topologically equivalent to an ellipse (into which it can be deformed by stretching) and a sphere is equivalent to an ellipsoid.
What is another word for topology?
What is another word for topology?
| geography | chorography |
|---|---|
| geomorphology | cartography |
| geology | physiography |
| earth science |
What is a topology simple definition?
A network topology is the physical and logical arrangement of nodes and connections in a network. Nodes usually include devices such as switches, routers and software with switch and router features. Network topologies are often represented as a graph.
What objects are topologically equivalent?
Definition. Two figures are topologically equivalent if if one figure can be transformed into the other by twisting and stretching, but not tearing, cutting, or gluing.
What is meant by metric equivalent?
Metric equivalence is a quantitative way to assess cross-cultural equivalences of translated instruments by examining the patterns of psychometric properties based on cross-cultural data derived from both versions of the instrument.
Which two of the following compartments are topologically equivalent?
ER and Golgi is topologically equivalent to the outside of the cell.
What space inside the cell is topologically equivalent to the cytoplasm?
The cytoplasm and the nucleus are said to be topologically equivalent because the outer and inner nuclear membranes are continuous with one another, so that the flow of material between the nucleus and cytosol occurs without crossing a lipid bilayer.
Are a sphere and a torus topologically equivalent?
1. The sphere and torus are topologically distinct. On the surface of a donut there are loops one can draw that do not separate the surface into disjoint pieces.
What is the opposite of topology?
Indiscrete spaces In some ways, the opposite of the discrete topology is the trivial topology (also called the indiscrete topology), which has the fewest possible open sets (just the empty set and the space itself).
Are all metrics equivalent?
In finite dimensional spaces, all metrics induced by the p-norm, including the euclidean metric, the taxicab metric, and the Chebyshev distance, are strongly equivalent.
What is topologically equivalent to cytosol?
Which compartment is topologically equivalent with the Golgi?
What is topological equivalence?
topological equivalence. noun. : the relationship of two geometric figures capable of being transformed one into the other by a one-to-one transformation continuous in both directions.
How do you know if two spaces are topologically equivalent?
Two spaces are called topologically equivalent if there exists a homeomorphism between them. The properties of size and straightness in Euclidean space are not topological properties, while the connectedness of a figure is. Any simple polygon is homeomorphic to a circle; all figures homeomorphic to a circle are called…
What is a topological space?
A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology.
What are the properties of topology?
These properties include openness, nearness, connectedness, and continuity. b. The underlying structure that gives rise to such properties for a given figure or space: The topology of a doughnut and a picture frame are equivalent. 4. ComputersThe arrangement in which the nodes of a network are connected to each other.