拓扑群中的离散子集与可数拓扑不连通群
Discrete Subsets in Topological Groups and Countable Extremally Disconnected Groups
摘要：
证明了单位元邻域滤子不快速的可数拓扑群包含一个恰有一个非孤立点的离散集。这给出了一个否定的答案Protasov的问题存在ZFC的可数非离散群，其中所有离散子集是封闭的。还证明了可数非离散极端不连通群的存在性蕴含着快速超滤子的存在性，因此在ZFC中不能构造可数非离散极端不连通群.
英文摘要：
It is proved that any countable topological group in which the filter of neighborhoods of the identity element is not rapid contains a discrete set with precisely one nonisolated point. This gives a negative answer to Protasov's question on the existence in ZFC of a countable nondiscrete group in which all discrete subsets are closed. It is also proved that the existence of a countable nondiscrete extremally disconnected group implies the existence of a rapid ultrafilter and, hence, a countable nondiscrete extremally disconnected group cannot be constructed in ZFC.
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。
