Topology (topology v0.1.2)
Returns a topology of the given set.
Link to this section Summary
Functions
Returns a discrete space of the given set.
Returns a discreate topology of the given set.
Returns a discrete space of the given set.
Returns a indiscreate topology of the given set.
Returns a topological spaces of the given set.
Returns a topology of the given set.
Link to this section Functions
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closed_set_system(arg)
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discrete_space(set)
Returns a discrete space of the given set.
examples
Examples
iex> Topology.discrete_space(MapSet.new([:a, :b]))
{MapSet.new([:a, :b]), MapSet.new([MapSet.new([]), MapSet.new([:a]), MapSet.new([:b]), MapSet.new([:a, :b])])}
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discrete_topology(set)
Returns a discreate topology of the given set.
examples
Examples
iex> Topology.discrete_topology(MapSet.new([:a, :b]))
MapSet.new([MapSet.new([]), MapSet.new([:a]), MapSet.new([:b]), MapSet.new([:a, :b])])
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indiscrete_space(set)
Returns a discrete space of the given set.
examples
Examples
iex> Topology.indiscrete_space(MapSet.new([:a, :b]))
{MapSet.new([:a, :b]), MapSet.new([MapSet.new([]), MapSet.new([:a, :b])])}
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indiscrete_topology(set)
Returns a indiscreate topology of the given set.
examples
Examples
iex> Topology.indiscrete_topology(MapSet.new([:a, :b]))
MapSet.new([MapSet.new(), MapSet.new([:a, :b])])
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is_closed_set?(set, arg)
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is_open_set?(set, arg)
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open_set_systems(set)
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topological_spaces(set)
Returns a topological spaces of the given set.
examples
Examples
iex> Topology.topological_spaces(MapSet.new([:a, :b]))
[
{MapSet.new([:a, :b]), MapSet.new([MapSet.new([]), MapSet.new([:a, :b])])},
{MapSet.new([:a, :b]), MapSet.new([MapSet.new([]), MapSet.new([:a]), MapSet.new([:a, :b])])},
{MapSet.new([:a, :b]), MapSet.new([MapSet.new([]), MapSet.new([:b]), MapSet.new([:a, :b])])},
{MapSet.new([:a, :b]), MapSet.new([MapSet.new([]), MapSet.new([:a]), MapSet.new([:b]), MapSet.new([:a, :b])])}
]
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topologies(set)
Returns a topology of the given set.
examples
Examples
iex> Topology.topologies(MapSet.new([:a, :b]))
MapSet.new([
MapSet.new([MapSet.new([]), MapSet.new([:a, :b])]),
MapSet.new([MapSet.new([]), MapSet.new([:a]), MapSet.new([:a, :b])]),
MapSet.new([MapSet.new([]), MapSet.new([:b]), MapSet.new([:a, :b])]),
MapSet.new([
MapSet.new([]),
MapSet.new([:a]),
MapSet.new([:b]),
MapSet.new([:a, :b])
])
])