Why is topology called 位相幾何学?


Topology in English is called
[位相幾何学](http://ja.wikipedia.org/wiki/%E4%BD%8D%E7%9B%B8%E5%B9%BE%E4%BD%95%E5%AD%A6)
in Japanese; also, topological space is called
[位相空間](http://ja.wikipedia.org/wiki/%E4%BD%8D%E7%9B%B8%E7%A9%BA%E9%96%93). 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`?




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.




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.

