| 21. | The Hilbert cube is obtained by taking a topological product of countably many copies of the unit interval.
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| 22. | "Standard " are called those MTL-algebras whose lattice reduct is the real unit interval [ 0, 1 ].
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| 23. | Specifically, it is a nontrivial bundle over the circle " S " 1 with a fiber the unit interval,.
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| 24. | Let's assume our coordinates are in the unit interval [ 0, 1 ) just divide yours by 2 8.
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| 25. | This integral is also self-similar on the unit interval, under an action of the same dyadic monoid as described above.
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| 26. | Let " U " be a random variable that is uniformly distributed on the unit interval [ 0, 1 ].
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| 27. | Re-writing the above to make the action of " g " more clear : on the unit interval, one has
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| 28. | By the intermediate value theorem, the image of " X " under this continuous function is the entire unit interval.
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| 29. | Assuming the axiom of choice, there are subsets of the unit interval for which the Banach Mazur game is not determined.
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| 30. | Both trigonometric and Walsh systems admit natural extension by periodicity from the unit interval to the real line \ mathbb R.
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