Review Note
Last Update: 04/24/2024 02:36 AM
Current Deck: Topology
PublishedCurrently Published Content
Equivalence 1
Standard definition:
\([\forall y \in y][\exists x \in X][f(x) = y]\)
\([\forall y \in y][\exists x \in X][f(x) = y]\)
Equivalence 2
The preimage of any element of the codomain is nonempty:
\([\forall y \in Y ][\exists x\in X] [x \in f^{-1}(y) ]\)
\([\forall y \in Y ][\exists x\in X] [x \in f^{-1}(y) ]\)
Equivalence 3
\(f\) is an epimorphism/right-cancellative:
\(g \circ f = h \circ f \implies g = h\)
\(g \circ f = h \circ f \implies g = h\)
Equivalence 4
Equivalence 5
Premise 1
\(f:X\to Y\) is a function
Premise 2
Premise 3
Premise 4
Name
Surjective function (3 Definitions)
Context
Set Theory
Subcontext
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