Examples of 'are homeomorphic' in a sentence
Meaning of "are homeomorphic"
are homeomorphic - in mathematics, indicating that two objects or spaces are related through a continuous transformation
How to use "are homeomorphic" in a sentence
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are homeomorphic
Determining whether two finite simplicial complexes are homeomorphic.
If two spaces are homeomorphic then they have exactly the same topological properties.
Two smooth surfaces are diffeomorphic if and only if they are homeomorphic.
These are precisely the spaces that are homeomorphic to the Stone spaces of Boolean algebras.
Prove that any two finite open intervals are homeomorphic.
The equivalence classes are homeomorphic to a single point, a compact interval or a ray.
We know that two topological spaces are equivalent if they are homeomorphic.
The loops are homeomorphic to circles, although they are not geometric circles.
Any two discrete spaces with the same cardinality are homeomorphic.
Thus, a square and a circle are homeomorphic to each other, but a sphere and a torus are not.
Two open meanders are said to be equivalent if they are homeomorphic in the plane.
Thus, a square and a circle are homeomorphic to each other, but a sphere and a donut are not.
One can ask whether all contractible manifolds are homeomorphic to a ball.
If $ X $ and $ Y $ are homeomorphic then their fundamental groups are isomorphic.
Two topological spaces carrying the trivial topology are homeomorphic iff they have the same cardinality.
See also
A major focus of knot theory is to determine whether two different-looking knots are homeomorphic.
Consequently, two closed oriented 2-manifolds are homeomorphic if and only if they are diffeomorphic.
If closed 2-manifolds M and N are homotopically equivalent then they are homeomorphic.
For example, the interval ( 0, 1 ) and the whole of R are homeomorphic under the usual topology.
Thus two simply-connected closed smooth 4-manifolds with the same intersection form are homeomorphic.
For example, a square and a circle are homeomorphic.
Problems in topology = = * Determining whether two finite simplicial complexes are homeomorphic.
Two semi-meanders are said to be equivalent if they are homeomorphic in the plane.
However, the underlying topological spaces within the Möbius strip are homeomorphic in each case.
In particular, if and are isometric, then and are homeomorphic.
