Seonglae ChoA topological space that is locally similar to Euclidean space
Like measuring the distance between 3 o'clock and 9 o'clock on a clock face not as a straight line but as an arc along the circle, it is 1-dimensional rather than 2-dimensional
Manifold Notion
- 1d manifold
- 2d manifold
- 3d manifold
Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an -dimensional manifold, or -manifold for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of -dimensional Euclidean space.
https://en.wikipedia.org/wiki/Manifold
brain
Figure 2-5: Topologically folded surface of brain and close-up...
Download scientific diagram | Topologically folded surface of brain and close-up tessellation of a small selected region (white arrow)[20]. from publication: Persistent Homology for Image Analysis | Topological Data Analysis (TDA) is a new field of mathematics emerged rapidly since the first decade of the century from various works of algebraic topology and geometry. The goal of TDA and its main tool of persistent homology (PH) is to provide topological insight into... | Images, Image Analysis and LBP | ResearchGate, the professional network for scientists.
https://www.researchgate.net/figure/Topologically-folded-surface-of-brain-and-close-up-tessellation-of-a-small-selected_fig5_341136357