Images of Manifold Subsets under Continuous Maps as Subsets of the Codomain - Manifolds

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# Images of Manifold Subsets under Continuous Maps as Subsets of the Codomain

`ImageManifoldSubset` implements the image of a continuous map \(\Phi\) from a manifold \(M\) to some manifold \(N\) as a subset \(\Phi(M)\) of \(N\), or more generally, the image \(\Phi(S)\) of a subset \(S \subseteq M\) as a subset of \(N\).

class sage.manifolds.continuous_map_image.ImageManifoldSubset(map, inverse=None, name=None, latex_name=None, domain_subset=None)

  Bases: `ManifoldSubset`

  Subset of a topological manifold that is a continuous image of a manifold subset.

  INPUT:

  - `map` – continuous map \(\Phi\)

  - `inverse` – (default: `None`) continuous map from `map.codomain()` to `map.domain()`, which once restricted to the image of \(\Phi\) is the inverse of \(\Phi\) onto its image if the latter exists (NB: no check of this is performed)

  - `name` – (default: computed from the names of the map and the subset) string; name (symbol) given to the subset

  - `latex_name` – string (default: `None`); LaTeX symbol to denote the subset; if none is provided, it is set to `name`

  - `domain_subset` – (default: the domain of `map`) a subset of the domain of `map`