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Topology in English is called 位相幾何学 in Japanese; also, topological space is called 位相空間. But why is topology called 位相幾何学? What is the correspondence between topo and 位相? What is the origin of 位相?

ssb
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Popopo
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  • There might not be a direct correspondence. I don't see one between [topo-](http://www.etymonline.com/index.php?allowed_in_frame=0&search=topo-&searchmode=none) and 位相, nor between [-logy](http://www.etymonline.com/index.php?term=-logy&allowed_in_frame=0) and 幾何学. Good question, though! –  Apr 02 '13 at 13:20
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    Not related to your specific question, but I really like [this question](http://japanese.stackexchange.com/questions/2416/the-etymology-of-%E9%96%A2%E6%89%8B%E3%80%90%E3%81%8B%E3%82%93%E3%81%97%E3%82%85%E3%80%91) about the origin of mathematical terminology in Japanese (in this case the origin of "functor"). – Earthliŋ Apr 02 '13 at 13:44
  • @snailplane Although the subject is called 位相幾何学, the concept of a [topology](http://en.wikipedia.org/wiki/Topological_space#Open_sets_definition) (as in collection of open sets) is just called 位相 in Japanese. So we really need a correspondence 位相 <=> topology. – Earthliŋ Apr 03 '13 at 14:04
  • Recall that in English, names of disciplines often stand for the objects they study, where as in Japanese, they have different names. Thus _topology_ can be translated in Japanese 位相 or 位相幾何学, depending on the context. To make things more complicated, _topology_ usually stands for application of topological notions to geometry, not a study of topological spaces themselves (which is usually called general topology or point-set topology), which is why the word 幾何 comes into play. – Pteromys Aug 16 '13 at 15:12

1 Answers1

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The correspondence isn't direct; if 位相幾何学 were loan translated into English it would be 位相 (topological) 幾何学 (geometry).

Interestingly, though, 位相 means phase (i.e. of a sinusoidal function) as well as topology, and that means that the term 位相空間 is ambiguous between phase space (in physics) and topological space (in mathematics).

EDIT: To clarify the etymology:

The first morpheme in topology is Gk. τόπος 'place', which corresponds to 位 (position). I would suggest that 相 in this context means 'aspect', 'behaviour', and not 'mutual' (its other sense). In Chinese, the two senses of 相 have different readings (xiang4 vs xiang1). Putting it all together, the term 位相 refers to the disposition of place -- that is, how the place is arranged; in other words, its topology.

jogloran
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    But where does the term 位相 come from? – ssb Apr 02 '13 at 14:33
  • A bit of googling reveals that there are other usages of the word 位相, such as [this](http://dictionary.sanseido-publ.co.jp/wp/2007/12/19/%E6%BC%A2%E5%AD%97%E3%81%AE%E7%8F%BE%E5%9C%A8%EF%BC%9A%E3%80%8C%E4%BD%8D%E7%9B%B8%E6%96%87%E5%AD%97%E3%80%8D%E3%81%A8%E5%9B%BD%E8%AA%9E%E8%BE%9E%E5%85%B8/) I'm curious where the word came from, too. – Kohsuke Kawaguchi Apr 02 '13 at 15:01
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    The first morpheme in *topology* is Gk. τόπος 'place', which corresponds to 位 (position). I would suggest that 相 in this context means 'aspect', 'behaviour', and not 'mutual' (its other sense). In Chinese, the two senses of 相 have different readings (*xiang4* vs *xiang1*). Putting it all together, the term 位相 refers to the disposition of place -- that is, how the place is arranged; in other words, its topology. – jogloran Apr 03 '13 at 02:38
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    Thanks, but there is one point remained unclear to me:what is 'position' in topology? A topological space merely defined by 'what is open set', whereas 'position' seems need to be defined in vector space... – Popopo Apr 03 '13 at 15:15
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    @Popopo: Euler referred to early topological concepts as constituting a *geometria situs* (geometry of place) as opposed to physical geometry which accounts for lengths and distances, and the Japanese is a precise calque of this. – jogloran Apr 04 '13 at 00:44