### Definition/Summary:

Mathematics

Manifold

- Topological space that resembles Euclidean space near each point
- Each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n

### Expanded info:

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Markov chain

- Usually discrete stochastic process (as a random walk) in which the probabilities of occurrence of various future states depend only on the present state of the system or on the immediately preceding state and not on the path by which the present state was achieved