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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: 572
Registered: 12/18/07
Re: Mapping from straight line to straight line
Posted: Nov 3, 2013 9:17 AM
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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?

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.

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

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