We classify and explicitly describe maximal antipodal sets of some compact classical symmetric spaces and those of their quotient spaces by making use of suitable embeddings of these symmetric spaces into compact classical Lie groups. We give the cardinalities of maximal antipodal sets and we determine the maximum of the cardinalities and maximal antipodal sets whose cardinalities attain the maximum.

中文翻译：

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紧致经典对称空间的最大对映集及其基数I

我们通过利用紧凑型经典对称空间的适当嵌入将这些对称空间的最大对映集及其商空间进行分类，并对其进行了明确描述。我们给出最大对映集的基数，并确定基数和其基数达到最大值的最大对映集的最大值。