In this paper, we study the topological structure on Ext-groups of unital extensions. It is proved that the stable strong Ext-group and the stable weak Ext-group for unital extensions are pseudopolish groups if A is a unital $$C^*$$-algebra in the bootstrap class $${{\mathcal {N}}}$$ and B is a stable separable $$C^*$$-algebra. Furthermore, we topologize certain UCTs and prove that these UCTs are exact sequences as topological groups.

中文翻译：

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单元扩展的拓扑 UCT

在本文中，我们研究了单元扩展的 Ext 群的拓扑结构。证明了如果A是自举类$${{\mathcal {N}中的单位$$C^*$$-代数，则单位扩展的稳定强Ext-群和稳定弱Ext-群是伪抛光群}}$$ 和 B 是稳定可分离的 $$C^*$$-代数。此外，我们对某些 UCT 进行拓扑并证明这些 UCT 是作为拓扑组的精确序列。