局部预紧群：（局部）实紧性与连通性
Locally precompact groups: (Local) realcompactness and connectedness
摘要：
A. Weil断言一个拓扑群嵌入一个局部紧群的（稠密）子群当且仅当它包含一个非空的预紧开集;这样的群被称为局部预紧群。在局部预紧群类中，作者将具有以下拓扑性质的群分类：迪厄多内完备性;局部实紧性;实紧性;遗传实紧性;连通性;局部连通性;零维性。他们还证明了一个阿贝尔局部预紧群作为一个拓扑群的拟分支出现当且仅当它是预紧生成的，也就是说，它是由一个预紧子集代数生成的。
英文摘要：
A theorem of A. Weil asserts that a topological group embeds as a (dense) subgroup of a locally compact group if and only if it contains a non-empty precompact open set; such groups are called locally precompact. Within the class of locally precompact groups, the authors classify those groups with the following topological properties: Dieudonné completeness; local realcompactness; realcompactness; hereditary realcompactness; connectedness; local connectedness; zero-dimensionality. They also prove that an abelian locally precompact group occurs as the quasi-component of a topological group if and only if it is precompactly generated, that is, it is generated algebraically by a precompact subset.
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