Search results
Results from the WOW.Com Content Network
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 .
In cartography, geology, and robotics, [1] a topological map is a type of diagram that has been simplified so that only vital information remains and unnecessary detail has been removed. These maps lack scale, also distance and direction are subject to change and/or variation, but the topological relationship between points is maintained.
In mathematics, more specifically in topology, an open map is a function between two topological spaces that maps open sets to open sets. [1] [2] [3] That is, a function : is open if for any open set in , the image is open in . Likewise, a closed map is a function that maps closed sets to closed sets.
Geospatial topology is the study and application of qualitative spatial relationships between geographic features, or between representations of such features in geographic information, such as in geographic information systems (GIS). [1]
Topological geometry deals with incidence structures consisting of a point set and a family of subsets of called lines or circles etc. such that both and carry a topology and all geometric operations like joining points by a line or intersecting lines are continuous.
Let M be a topological space.A chart (U, φ) on M consists of an open subset U of M, and a homeomorphism φ from U to an open subset of some Euclidean space R n.Somewhat informally, one may refer to a chart φ : U → R n, meaning that the image of φ is an open subset of R n, and that φ is a homeomorphism onto its image; in the usage of some authors, this may instead mean that φ : U → R n ...
Regular maps of the form {4,4} m,0 can be represented as the finite regular skew polyhedron {4,4 | m}, seen as the square faces of a m×m duoprism in 4-dimensions. Here's an example {4,4} 8,0 mapped from a plane as a chessboard to a cylinder section to a torus. The projection from a cylinder to a torus distorts the geometry in 3 dimensions, but ...
The class of all pointed spaces forms a category Top with basepoint preserving continuous maps as morphisms. Another way to think about this category is as the comma category , ( { ∙ } ↓ {\displaystyle \{\bullet \}\downarrow } Top ) where { ∙ } {\displaystyle \{\bullet \}} is any one point space and Top is the category of topological spaces .