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I'm looking for a word to describe a function where every output is guaranteed to have come from exactly one contiguous range of input values.

For example, a monotonic function has this property, but that is too strong: the relative ordering is unimportant.

However, this is a looser guarantee than that the function be invertible. It's not necessary that it be possible to deduce exactly what the input was for a given output.

For example, a function which produced these results might qualify:

x    y
------
0    0
1    0
2    0
3    2
4    2
5    2
6    1
7    1

But a function that produced these results would not:

x    y
------
0    0
1    0
2    0
3    2
4    3
5    2
6    1
7    1

because 2 no longer only occurs within a single range of input values.

lemnar
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    A lemnar function? – Andrea Feb 09 '16 at 09:00
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    As a generalization of injective function (usually called “one to one” or shortly “1-1”) it has been used “many-one”. In your case, for each output a there is a range, or an interval of numbers. So a suggestion could be “interval to one function”.

    Another option could be “preconnected” function; if you use your definition in the real numbers, the intervals are connected, and the pre-image of each point must be a connected subset.

     – Pedro Sánchez Terraf Feb 12 '16 at 20:29
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    Following Pedro's first observation, I half-jokingly suggest interjective :P – Eric Stucky Feb 14 '16 at 21:09
  • @Pedro Sánchez Terraf: your comment contains a good answer. Please include your answer in an answer. – Kyle Thomas Sep 01 '16 at 17:50
  • @aLoveOfSurf Really? Perhaps I can put it as an answer, specially because there are no others. – Pedro Sánchez Terraf Sep 01 '16 at 20:01

1 Answers1

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Following @aLoveOfSurf suggestion, I'm making my comment into an answer. Nevertheless, I must disclaim that I don't know about any established terminology for this kind of functions.

As a generalization of injective function (usually called “one to one” or shortly “1-1”) it has been used “many-one”. In your case, for each output a there is a range, or an interval of numbers. So a suggestion could be “interval to one function”. Another option could be “preconnected” function; if you use your definition in the real numbers, the intervals are connected, and the pre-image of each point must be a connected subset.

Pedro Sánchez Terraf
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