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Topic: Mapping from straight line to straight line
Replies: 11   Last Post: Nov 3, 2013 4:35 PM

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Timothy Murphy

Posts: 496
Registered: 12/18/07
Re: Mapping from straight line to straight line
Posted: Nov 3, 2013 4:35 PM
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Virgil wrote:

> In article <l55lui$t76$1@dont-email.me>,
> Timothy Murphy <gayleard@eircom.net> wrote:
>

>> emwong wrote:
>>

>> > I am not sure whether I understand you correctly. Does the proof uses
>> > the assumption that the map sends parallel lines to parallel lines?

>>
>> Yes.
>> When you say that a map T sends straight lines into straight lines,
>> I take it this means that all the points of l are mapped into
>> all the points of T(l).
>> In that case, if T(l) and T(m) meet in P
>> then P must be on l and m, which therefore are not parallel.


> But in spaces of 3 or more dimensions there are non-parallel lines which
> do not intersect.


True. I should have said that I was considering the 2-dimensional case.
In the construction I gave everything was in one plane.

> --
--
Timothy Murphy
e-mail: gayleard /at/ eircom.net
School of Mathematics, Trinity College, Dublin 2, Ireland




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