# 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)

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