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This approach allows us to deduce results for metric spaces from the corresponding result in the fuzzy setting.

Actually we deduce these results from a slightly more general technical theorem for C∗-algebras endowed with gauge actions and fixed point algebra AF, among other requirements.

We deduce some results from Theorem 2.1 as follows.

We deduce the result from (i). □.

Hence, we can deduce the result from Lemma 2.

We further deduce the following results from Corollary 2. ([24], p.573).

As a consequence of the observation above, one can deduce the following results from Theorem 2.1.

In particular, if (T x)=C) for any (xin C), then we can deduce the following results from Theorem 3.1 and Theorem 3.2.

These results were compared with a number of values determined experimentally in the ternary system and with values deduced from results obtained for LiClAlCl3 and KClAlCl3 binary systems.

The stress-intensity factor for such problem in an elastic medium can be deduced from results obtained in this paper.

However, an obvious problem when population history is deduced from results with extant human material is that important information regarding population replacements and minor migration events is missed, if genetic information has been lost over long periods of time.

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