Basic Results on Coxeter Sets

Corollary 3.5.4 For each closed subset T of (L), we have the following. 

(i) Considering Lemma 2.5.9(ii) we obtain from Lemma 3.5.3 that T C (LC T). Since T is assumed to be closed we also have that (LOT) C T. 

Prom Lemma 3.5.5(i) we obtain, in particular, that C),)( L)) is a closed subset of S. 

Throughout this section, the letter L stands for a set of involutions of S. Instead of we shall write t. 

In accordance with Section 3.4 we shall write, for each element s in (L), S i(s) instead of S s, L). 

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