| 41. | These conditions are very loose, and they allow enormous flexibility in the choice of open sets.
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| 42. | Every open set in the subshift of finite type is a countable union of cylinder sets.
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| 43. | The open intervals coincide with the open sets of the real line in its standard topology.
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| 44. | The 2002 Australian Open set records for the dearth of top-ranked men in the second week.
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| 45. | More precisely, one can use bounded continuous functions that vanish outside one of the open sets.
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| 46. | Once he had axiomatized the notion of covering, open sets could be replaced by other objects.
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| 47. | This algorithm begins with a start node and an " open set " of candidate nodes.
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| 48. | Under this definition the open sets of a neighbourhood space give rise to a topological space.
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| 49. | Closed sets are complements of open sets.
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| 50. | Each open set is determined by a ( possibly infinite ) union of nodes of that tree.
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