topology
public class FiniteSpace<E extends java.lang.Comparable<E>> extends java.lang.Object implements TopologicalSpace<E>
Constructor and Description |
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FiniteSpace()
Creates an empty space.
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FiniteSpace(FiniteSpace<E> space)
Creates a new finite topological space from a given finite space.
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FiniteSpace(java.util.Set<E> points,
BinaryRelation<E> rel)
Creates a space with given point set and binary relation.
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Modifier and Type | Method and Description |
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boolean |
addAllPair(java.util.Set<Pair<E,E>> s)
Adds a set of pairs to the topology-defining relation of a finite
topological space, if the pairs' key and value belong to the
point set.
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boolean |
addAllPoint(java.util.Set<E> pts)
Adds a set of points to the point set of a finite topological space.
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boolean |
addPair(Pair<E,E> e)
Adds a pair to the topology-defining relation of a
finite topological space, if the pair's key and value
belong to the point set.
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boolean |
addPoint(E e)
Adds a point to the point set of a finite topological space.
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java.util.Set<java.util.List<E>> |
allPaths(E source,
E destination)
Returns all paths from a source to a destination point.
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FiniteSpace<E> |
closure(E point)
Returns the closure of a point in this finite topological space.
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int |
dimension()
Returns the Krull dimension of this finite topological space.
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FiniteSpace<E> |
dual()
Returns the Alexandrov dual of this finite topological space.
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<F extends java.lang.Comparable<F>> |
equals(FiniteSpace<F> space)
Checks equality of this finite topological space with a given
finite topological space.
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java.util.Set<java.util.TreeSet<E>> |
fatPoints()
Returns the set of fat points of this finite topological space.
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java.util.Set<E> |
getPointSet()
Returns the point set underlying the topological space.
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BinaryRelation<E> |
getPreOrder()
Returns the reflexive and transitive closure of the
topology-defining relation.
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BinaryRelation<E> |
getRelation()
Returns the topology-defining relation.
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BinaryRelation<E> |
HasseDiagram()
Returns the Hasse diagram of the Kolmogorov quotient of this finite
topological space.
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boolean |
isTzero()
Returns true iff pre-order is antisymmetric.
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FiniteSpace<E> |
KolmogorovQuotient()
Returns the Kolmogorov Quotient of this finite topological space
by removing points.
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java.util.Set<E> |
KOpenPoints()
Returns the set of maximal elements of the Kolmogorov quotient of a
finite topological space.
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java.util.Set<E> |
KVertices()
Returns the set of minimal elements of the
Kolmogorov quotient of this finite topological space.
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FiniteSpace<E> |
neighbourhood(E point)
Returns the minimal open neighbourhood of a point in this
finite topological space.
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FiniteSpace<E> |
pClosure(E point)
Returns the punctured closure of a point in this
finite topological space.
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FiniteSpace<E> |
pNeighbourhood(E point)
Returns the punctured minimal open neighbourhood of a point in this
finite topological space.
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boolean |
removeAllPair(java.util.Set<Pair<E,E>> s)
Removes a set of pairs from the topology-defining relation.
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boolean |
removeAllPoint(java.util.Set<E> s)
Removes a set of points and updates the relation.
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boolean |
removePair(Pair<E,E> e)
Removes a pair from the topology-defining relation.
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boolean |
removePoint(E e)
Removes a point from the point set, and updates the relation.
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FiniteSpace<E> |
T0Space()
Returns the Kolmogorov quotient of this finite topological space, where
the relation is the Hasse diagram.
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public FiniteSpace()
public FiniteSpace(java.util.Set<E> points, BinaryRelation<E> rel)
E
- space typepoints
- a point setrel
- a relationpublic FiniteSpace(FiniteSpace<E> space)
E
- space typespace
- public java.util.Set<E> getPointSet()
getPointSet
in interface TopologicalSpace<E extends java.lang.Comparable<E>>
public BinaryRelation<E> getRelation()
getRelation
in interface TopologicalSpace<E extends java.lang.Comparable<E>>
public <F extends java.lang.Comparable<F>> boolean equals(FiniteSpace<F> space)
F
- space typespace
- public BinaryRelation<E> getPreOrder()
E
- relation typepublic boolean isTzero()
isTzero
in interface TopologicalSpace<E extends java.lang.Comparable<E>>
public boolean addPoint(E e)
e
- a pointpublic boolean addAllPoint(java.util.Set<E> pts)
pts
- a set of pointspublic boolean addPair(Pair<E,E> e)
e
- a pairpublic boolean addAllPair(java.util.Set<Pair<E,E>> s)
s
- a set of pairspublic boolean removePair(Pair<E,E> e)
e
- a pairpublic boolean removeAllPair(java.util.Set<Pair<E,E>> s)
s
- a set of pairspublic boolean removePoint(E e)
e
- a pointpublic boolean removeAllPoint(java.util.Set<E> s)
s
- a set of pointspublic java.util.Set<java.util.List<E>> allPaths(E source, E destination)
source
- destination
- public java.util.Set<java.util.TreeSet<E>> fatPoints()
public FiniteSpace<E> KolmogorovQuotient()
E
- space typepublic FiniteSpace<E> dual()
E
- space typepublic BinaryRelation<E> HasseDiagram()
E
- space typepublic FiniteSpace<E> T0Space()
E
- space typepublic int dimension()
public FiniteSpace<E> neighbourhood(E point)
E
- space typepoint
- public FiniteSpace<E> pNeighbourhood(E point)
E
- space typepoint
- public FiniteSpace<E> closure(E point)
E
- space typepoint
- public FiniteSpace<E> pClosure(E point)
E
- space typepoint
- public java.util.Set<E> KVertices()
E
- space typepublic java.util.Set<E> KOpenPoints()
E
- space type