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Что (кто) такое N-connected space - определение
N-connected space
In the mathematical branch of algebraic topology, specifically homotopy theory, n-connectedness (sometimes, n-simple connectedness) generalizes the concepts of path-connectedness and simple connectedness. To say that a space is n-connected is to say that its first n homotopy groups are trivial, and to say that a map is n-connected means that it is an isomorphism "up to dimension n, in homotopy".
Simply connected space
TOPOLOGICAL SPACE WHICH HAS NO HOLES THROUGH IT
Simply-connected; Multiply connected; Multiply-connected; Doubly connected; Singly connected; Simply connected set; 1-Connected; 1-connected; Simply-connected set; Simply-connected domain; Simply connected domain; Simply connected; Non-simply-connected; Simply Connected; Simply connected topological space
In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question. The fundamental group of a topological space is an indicator of the failure for the space to be simply connected: a path-connected topological space is simply connected if and only if its fundamental group is trivial.
Semi-locally simply connected
![The [[Hawaiian earring]] is not semi-locally simply connected.](https://commons.wikimedia.org/wiki/Special:FilePath/Hawaiian earrings.svg?width=200 "The [[Hawaiian earring]] is not semi-locally simply connected.")
In mathematics, specifically algebraic topology, semi-locally simply connected is a certain local connectedness condition that arises in the theory of covering spaces. Roughly speaking, a topological space X is semi-locally simply connected if there is a lower bound on the sizes of the “holes” in X.
