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Alex M.
Alex M.
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Is a LOTStotally ordered, separable and connected topological space metrizable (in the order topology)?

Is a LOTStotally ordered, separable and connected topological space metrizable (in the order topology)?

If we relax the assumption of connectedness, I know the counterexamples, but if we have a linear continuum that is also separable, can we say it is metrizable?

Thanks!

Is a LOTS, separable and connected space metrizable?

Is a LOTS, separable and connected space metrizable?

Thanks!

Is a totally ordered, separable and connected topological space metrizable (in the order topology)?

Is a totally ordered, separable and connected topological space metrizable (in the order topology)?

If we relax the assumption of connectedness, I know the counterexamples, but if we have a linear continuum that is also separable, can we say it is metrizable?

Thanks!

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Crash Bandicoot
Crash Bandicoot
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Is a totally orderedLOTS, separable and connected topological space metrizable (in the order topology)?

Is a totally orderedLOTS, separable and connected topological space metrizable (in the order topology)?

If we relax the assumption of connectedness, I know the counterexamples, but if we have a linear continuum that is also separable, can we say it is metrizable?

Thanks!

Is a totally ordered, separable and connected topological space metrizable (in the order topology)?

Is a totally ordered, separable and connected topological space metrizable (in the order topology)?

If we relax the assumption of connectedness, I know the counterexamples, but if we have a linear continuum that is also separable, can we say it is metrizable?

Thanks!

Is a LOTS, separable and connected space metrizable?

Is a LOTS, separable and connected space metrizable?

Thanks!

Source Link
Crash Bandicoot
Crash Bandicoot
  • 327
  • 1
  • 8

Is a totally ordered, separable and connected topological space metrizable (in the order topology)?

Is a totally ordered, separable and connected topological space metrizable (in the order topology)?

If we relax the assumption of connectedness, I know the counterexamples, but if we have a linear continuum that is also separable, can we say it is metrizable?

Thanks!