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: sage.manifolds.subset.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 – (default: None) string; 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