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Structure-preserving Map
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Summary
A
Structure-preserving Map
is a function between two
Mathematical Structures
that maintains the
Operations and relations
of the structures, ensuring that the
Essential Properties
remain unchanged. These maps are crucial in various fields like algebra, topology, and geometry as they allow for the comparison and
Transfer of structures
in a
Consistent manner
.
Concepts
Homomorphism
Isomorphism
Endomorphism
Automorphism
Continuous Function
Linear Transformation
Functor
Natural Transformation
Diffeomorphism
Homeomorphism
Homomorphism Of Rings
Homomorphic Image
Relevant Degrees
Algebra 70%
Geometry 30%
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