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)

See Topology.topologies/1.

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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])
  ])
])