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 frommap.codomain()
tomap.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 toname
domain_subset
– (default: the domain ofmap
) a subset of the domain ofmap