| Real Line |
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| real numbers | |
| topological spaces | |
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However, this term is usually used when R is to be treated as a ''space'' of some sort, such as a Topological Space or a Vector Space . The real line has been studied at least since the days of the ancient Greeks, but it was not rigorously defined until 1872. Before and since that date, it has been a prolific example that has played a significant role in many branches of mathematics. The real line carries a standard Topology which can be introduced in two different, equivalent ways. First, since the real numbers are Totally Ordered , they carry an Order Topology . |
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