Difference between revisions of "Fibre"
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(Created page with "{{stub page|grade=A|msg=could use a reference}} ==Definition== Let {{M|f:X\rightarrow Y}} be a function, then: * A ''fibre'' of {{M|f}} is any set of the form {{M|f^{-1}(\...") |
(Added reference, see also, where to find another reference) |
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| − | {{stub page|grade=A|msg= | + | {{stub page|grade=A|msg=Could use another reference. I know {{link|An Introduction to Algebraic Topology - Joseph J. Rotman|ns=Books}} defines this term!}} |
==Definition== | ==Definition== | ||
| − | Let {{M|f:X\rightarrow Y}} be a [[function]], then: | + | Let {{M|f:X\rightarrow Y}} be a [[function]], then{{rITTMJML}}: |
* A ''fibre'' of {{M|f}} is any set of the form {{M|f^{-1}(\{y\})}} for some {{M|y\in Y}} | * A ''fibre'' of {{M|f}} is any set of the form {{M|f^{-1}(\{y\})}} for some {{M|y\in Y}} | ||
| + | ==See also== | ||
| + | * [[Level set]] - a similar concept, rarely used in the same context as a fibre however | ||
| + | * {{link|Saturated|map}} - generalisation of fibre. {{M|U\in\mathcal{P}(X)}} is ''saturated with respect to {{M|f}}'' if there is a subset, {{M|V\in\mathcal{P}(Y)}} such that {{M|1=U=f^{-1}(V)}} | ||
==References== | ==References== | ||
<references/> | <references/> | ||
{{Function terminology navbox|plain}} | {{Function terminology navbox|plain}} | ||
{{Definition|Set Theory|Elementary Set Theory}} | {{Definition|Set Theory|Elementary Set Theory}} | ||
Latest revision as of 12:59, 16 October 2016
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Could use another reference. I know An Introduction to Algebraic Topology - Joseph J. Rotman defines this term!
Definition
Let [ilmath]f:X\rightarrow Y[/ilmath] be a function, then[1]:
- A fibre of [ilmath]f[/ilmath] is any set of the form [ilmath]f^{-1}(\{y\})[/ilmath] for some [ilmath]y\in Y[/ilmath]
See also
- Level set - a similar concept, rarely used in the same context as a fibre however
- Saturated - generalisation of fibre. [ilmath]U\in\mathcal{P}(X)[/ilmath] is saturated with respect to [ilmath]f[/ilmath] if there is a subset, [ilmath]V\in\mathcal{P}(Y)[/ilmath] such that [ilmath]U=f^{-1}(V)[/ilmath]
References
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