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)[source]¶
Bases:
ManifoldSubsetSubset 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 subsetlatex_name– string (default:None); LaTeX symbol to denote the subset; if none is provided, it is set tonamedomain_subset– (default: the domain ofmap) a subset of the domain ofmap