enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Topological manifold - Wikipedia

    en.wikipedia.org/wiki/Topological_manifold

    It is common to place additional requirements on topological manifolds. In particular, many authors define them to be paracompact [3] or second-countable. [2] In the remainder of this article a manifold will mean a topological manifold. An n-manifold will mean a topological manifold such that every point has a neighborhood homeomorphic to R n.

  3. Manifold - Wikipedia

    en.wikipedia.org/wiki/Manifold

    A topological manifold looks locally like a Euclidean space in a rather weak manner: while for each individual chart it is possible to distinguish differentiable functions or measure distances and angles, merely by virtue of being a topological manifold a space does not have any particular and consistent choice of such concepts. [7]

  4. List of manifolds - Wikipedia

    en.wikipedia.org/wiki/List_of_manifolds

    Real line, R; Real projective line, RP 1 ≅ S 1; 2-manifolds. Cylinder, S 1 × R; ... Topological manifold; Manifolds with additional structure. Almost complex manifold;

  5. Classification of manifolds - Wikipedia

    en.wikipedia.org/wiki/Classification_of_manifolds

    A topological manifold that is in the image of is said to "admit a differentiable structure", and the fiber over a given topological manifold is "the different differentiable structures on the given topological manifold". Thus given two categories, the two natural questions are:

  6. Surface (topology) - Wikipedia

    en.wikipedia.org/wiki/Surface_(topology)

    More generally, a (topological) surface with boundary is a Hausdorff topological space in which every point has an open neighbourhood homeomorphic to some open subset of the closure of the upper half-plane H 2 in C. These homeomorphisms are also known as (coordinate) charts. The boundary of the upper half-plane is the x-axis.

  7. Atlas (topology) - Wikipedia

    en.wikipedia.org/wiki/Atlas_(topology)

    In mathematics, particularly topology, an atlas is a concept used to describe a manifold. An atlas consists of individual charts that, roughly speaking, describe individual regions of the manifold. In general, the notion of atlas underlies the formal definition of a manifold and related structures such as vector bundles and other fiber bundles.

  8. List of topologies - Wikipedia

    en.wikipedia.org/wiki/List_of_topologies

    Extended real number line; Fake 4-ball − A compact contractible topological 4-manifold. House with two rooms − A contractible, 2-dimensional simplicial complex that is not collapsible. Klein bottle; Lens space; Line with two origins, also called the bug-eyed line − It is a non-Hausdorff manifold.

  9. Boundary (topology) - Wikipedia

    en.wikipedia.org/wiki/Boundary_(topology)

    Conversely, the boundary of a closed disk viewed as a manifold is the bounding circle, as is its topological boundary viewed as a subset of the real plane, while its topological boundary viewed as a subset of itself is empty. In particular, the topological boundary depends on the ambient space, while the boundary of a manifold is invariant.