Opened 5 years ago

# Topological manifolds: basics — at Version 3

Reported by: Owned by: egourgoulhon egourgoulhon major sage-7.1 geometry topological manifolds mmancini Eric Gourgoulhon N/A public/manifolds/top_manif_basics 89c063c7119f19497e3d21b2a5a9dcb0752122b0 #18175

This is the implementation of topological manifolds over a topological field K resulting from the SageManifolds project. See the meta-ticket #18528 for an overview. By topological manifold over a topological field K it is meant a second countable Hausdorff space M such that every point in M has a neighborhood homeomorphic to Kn, with the same non-negative integer n for all points.

This tickets implements the following Python classes:

• `TopManifold`: topological manifold over a topological field K
• `TopManifoldPoint`: point in a topological manifold
• `TopManifoldSubset`: generic subset of a topological manifold
• `TopManifoldOpenSubset`: open subset of a topological manifold
• `Chart`: chart of a topological manifold
• `RealChart`: chart of a topological manifold over the real field
• `CoordChange`: transition map between two charts of a topological manifold

`TopManifold` is intended to serve as a base class for specific manifolds, like smooth manifolds (K=R) and complex manifolds (K=C).

### comment:1 Changed 5 years ago by egourgoulhon

• Description modified (diff)

### comment:2 Changed 5 years ago by jhpalmieri

The phrase "manifold over a field K" sounds odd to me. Is it used in the literature? What if K is a finite field? It seems that if X is a finite discrete space, for every finite field F and for every non-negative integer n, then X is a manifold over F of dimension n: F and n play no role. (I'm assuming that finite fields have been given the discrete topology.)

I think you might say "topological manifold over a topological field K", since obviously the topology on K is critical. Or you could omit "over a field K", and mention in the documentation that users can specify a topological field (like \CC, rather than the default \RR) if they want.

### comment:3 Changed 5 years ago by egourgoulhon

• Description modified (diff)
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