User:IssaRice/Analogous results between subfields of math

Finiteness vs compactness

see https://www.math.ucla.edu/~tao/preprints/compactness.pdf

Injective iff surjective

• If A and B are finite sets that have the same cardinality, then $f:A\to B$ is injective iff surjective.
• If V and W are finite-dimensional vector spaces with the same dimension, then a linear map $T:V\to W$ is injective iff surjective.

See also

• https://machinelearning.subwiki.org/wiki/User:IssaRice/Subfield_of_math_as_study_of_concepts_preserved_under_transformation