实数集R上几个常见拓扑的比较

The Comparison for Some Common Topologies on Real Numbers R

给出了实数集R上的7个子集族,并证明它们是R的拓扑基,决定了R上7个不同的拓扑,同时还对这些拓扑进行了比较,得到它们之间粗细的确定关系。

This paper shows seven classes of sets of real numbers,and proves that these classes of sets are bases for some topologies on real numbers,they determine seven different topologies on real numbers.At the same time,the paper compares with these topologies,and summarizes the coarser or weaker relations between these topologies.