拓扑群III的长余极限：积与余积的同胚
Long colimits of topological groups III: Homeomorphisms of products and coproducts
摘要：
吉洪诺夫空间上的紧支集同胚群可以用多种方式拓扑化，包括作为具有给定紧支集的同胚群的上极限，或作为其斯通-切赫紧化的同胚群的子群。如果这两个拓扑重合，则称一个空间具有紧支撑同胚性质（CSHP）。给出了序拓扑下序数的有限积具有CSHP的充要条件。此外，还给出了空间的有限积和余积具有CSHP的必要条件。
英文摘要：
The group of compactly supported homeomorphisms on a Tychonoff space can be topologized in a number of ways, including as a colimit of homeomorphism groups with a given compact support, or as a subgroup of the homeomorphism group of its Stone-Čech compactification. A space is said to have the Compactly Supported Homeomorphism Property (CSHP) if these two topologies coincide. The authors provide necessary and sufficient conditions for finite products of ordinals equipped with the order topology to have CSHP. In addition, necessary conditions are presented for finite products and coproducts of spaces to have CSHP.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
