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This is a question on the borderline between mathematics and English. I wonder in mathematics, are there some general differences between concepts with base and with basis in their names? In other words, do you have some idea when to use which, because I often use one when the other is expected.

For example, a basis of a vector space and a base of a topology.

Thanks and regards!

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Admittedly both words are quite overloaded... – J. M. Oct 31 '11 at 17:49
J.M. probably means having many different meanings – user12205 Oct 31 '11 at 17:59
"All your basis" – The Chaz 2.0 Oct 31 '11 at 18:17
@Tim: It's a humourous reference to this. – joriki Oct 31 '11 at 18:24
I was in the middle of making a joke when my iPhone prematurely submitted the comment. Then I lost Internet connection! But joriki figured it out :) – The Chaz 2.0 Oct 31 '11 at 18:30
up vote 5 down vote accepted

From an interlingual perspective, it's anomalous that English has two different words for this. German has only "Basis" and French has only "base". These are applied without difference to vector spaces and topologies.

Math history isn't my strong point, but my impression is that topology was more strongly influenced by French mathematicians (Poincaré, Analysis Situs) and the theory of vector spaces was more strongly influenced by German mathematicians (Hilbert space, Hilbert basis). It may be just a coincidence, but it seems at least possible that the two slightly different words already existing in the English language were preferentially used to coincide with the language in which people were predominantly reading and writing about these things at the time.

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Nice! Didn't know there is some history behind. – Tim Oct 31 '11 at 19:18

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