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: - 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