topology
public class PointReductions extends java.lang.Object
Constructor and Description |
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PointReductions() |
Modifier and Type | Method and Description |
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static <E extends java.lang.Comparable<E>> |
downBeatPoints(FiniteSpace<E> space)
Returns the set of down beat points of the Kolmogorov quotient of
a finite topological space.
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static <E extends java.lang.Comparable<E>> |
isDownBeatPoint(FiniteSpace<E> space,
E point)
Returns true if the given point is a down beat point of the Kolmogorov
quotient of a given finite topological space.
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static <E extends java.lang.Comparable<E>> |
isDownWeakPoint(FiniteSpace<E> space,
E point)
Returns true if the given point is a down weak point of the
Kolmogorov quotient of a given finite topological space.
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static <E extends java.lang.Comparable<E>> |
isUpBeatPoint(FiniteSpace<E> space,
E point)
Returns true if the given point is an up beat point of the
Kolmogorov quotient of a given finite topological space.
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static <E extends java.lang.Comparable<E>> |
isUpWeakPoint(FiniteSpace<E> space,
E point)
Returns true if the given point is an up weak point of the
Kolmogorov quotient of a given finite topological space.
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static <E extends java.lang.Comparable<E>> |
noBeatPoint(FiniteSpace<E> space)
Returns true if the Kolmogorov quotient of a finite topological space
has no beat point.
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static <E extends java.lang.Comparable<E>> |
noWeakPoint(FiniteSpace<E> space)
Returns true if the Kolmogorov quotient of a
finite topological space has no weak point.
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static <E extends java.lang.Comparable<E>> |
removeBeatPoints(FiniteSpace<E> space)
Returns a 0-core of a the Kolmogorov quotient of a
finite topological space, i.e.
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static <E extends java.lang.Comparable<E>> |
removeWeakPoints(FiniteSpace<E> space)
Returns a 1-core of the Kolmogorov quotient of a finite topological
space, i.e.
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static <E extends java.lang.Comparable<E>> |
upBeatPoints(FiniteSpace<E> space)
Returns the set of up beat points of the Kolmogorov quotient of
a finite topological space.
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public static <E extends java.lang.Comparable<E>> boolean isUpBeatPoint(FiniteSpace<E> space, E point)
E
- space typespace
- point
- public static <E extends java.lang.Comparable<E>> boolean isDownBeatPoint(FiniteSpace<E> space, E point)
E
- space typespace
- point
- public static <E extends java.lang.Comparable<E>> boolean noBeatPoint(FiniteSpace<E> space)
E
- space typespace
- public static <E extends java.lang.Comparable<E>> java.util.Set<E> upBeatPoints(FiniteSpace<E> space)
E
- space typespace
- public static <E extends java.lang.Comparable<E>> java.util.Set<E> downBeatPoints(FiniteSpace<E> space)
E
- space typespace
- public static <E extends java.lang.Comparable<E>> FiniteSpace<E> removeBeatPoints(FiniteSpace<E> space)
E
- space typespace
- public static <E extends java.lang.Comparable<E>> boolean isUpWeakPoint(FiniteSpace<E> space, E point)
E
- space typespace
- point
- public static <E extends java.lang.Comparable<E>> boolean isDownWeakPoint(FiniteSpace<E> space, E point)
E
- space typespace
- point
- public static <E extends java.lang.Comparable<E>> boolean noWeakPoint(FiniteSpace<E> space)
E
- space typespace
- public static <E extends java.lang.Comparable<E>> FiniteSpace<E> removeWeakPoints(FiniteSpace<E> space)
E
- space typespace
-