Vipul: 2 revisions

2008-05-11T19:59:47Z

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Vipul at 21:13, 13 December 2007

2007-12-13T21:13:31Z

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			{{indispensable lemma}}

	==Statement==		==Statement==

Vipul at 21:02, 13 December 2007

2007-12-13T21:02:07Z

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==Statement==

The inclusion of two adjacent sides in the unit square is equivalent to the inclusion of ''one'' side in the unit square, viz., in the inclusion of <math>I</math> in <math>I \times I</math>.

An explicit [[isotopy]] can also be written down, which may be more convenient in some situations.

==Applications==

* The inclusion of a point in the unit interval is a cofibration. To prove this, we note that this boils down to proving that two adjacent sides of the square are a [[retract]] of the unit square, which, by the two sides lemma, is equivalent to requiring that <math>I</math> is a retract of <math>I \times I</math> which is clearly true.

The retraction from <math>I \times I</math> to two sides can also be written down explicitly; this is more useful at times.

==Related results==

* [[Three sides lemma]]

Two sides lemma - Revision history

Vipul: 2 revisions

Vipul at 21:13, 13 December 2007

Vipul at 21:02, 13 December 2007