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Topic: Order embedding
Replies: 8   Last Post: Sep 16, 2013 10:01 PM

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David Hartley

Posts: 463
Registered: 12/13/04
Re: Order embedding
Posted: Sep 16, 2013 3:33 PM
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In message <o19e391hgcgk4fv7bd126p7lsle5g9j89o@4ax.com>,
dullrich@sprynet.com writes
>>> f:X -> Y is an order embedding when
>>> for all x,y, (x <= y iff f(x) <= f(y)).


>I think no. Surely an embedding is required to be injective.

f(x) = f(y) => f(x) <= f(y) and f(y) <= f(x)
=> x <= y and y <= x
=> x = y

David Hartley

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