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Indeed, let be a totally ordered set.
Let X be a totally ordered set.
Let be a totally ordered subset of.
Let be a totally ordered subset of and consider.
Let be a totally ordered subset in, where is a directed set.
Let I be a totally ordered set, and let { x γ } γ ∈ I be a chain in ( X, ⪯ ).
Similar(46)
Conclusively, is a totally ordered subset.
Obviously, is a totally ordered set in.
Then X is a totally ordered, complete S-metric space.
Suppose that is a totally ordered set in.
Since is a totally ordered set, makes sense and (2.2).
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