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In real and functional analysis, equicontinuity is a concept which extends the notion of uniform continuity from a single function to collection of functions. Given ...

A handle is a topological structure which can be thought of as the object produced by puncturing a surface twice, attaching a zip around each puncture travelling in opposite ...

Given a smooth function f:R^n->R^n, if the Jacobian is invertible at 0, then there is a neighborhood U containing 0 such that f:U->f(U) is a diffeomorphism. That is, there is ...

A singular point such that every neighborhood of the point intersects itself. Pinch points are also called Whitney singularities or branch points.

A real function is said to be analytic if it possesses derivatives of all orders and agrees with its Taylor series in a neighborhood of every point.

X subset= R^n is semianalytic if, for all x in R^n, there is an open neighborhood U of x such that X intersection U is a finite Boolean combination of sets {x^_ in ...

A Cantor set C in R^3 is said to be scrawny if for each neighborhood U of an arbitrary point p in C, there is a neighborhood V of p such that every map f:S^1->V subset C ...

Consider the local behavior of a map f:R^m->R^n by choosing a point x in R^m and an open neighborhood U subset R^m such that x in U. Now consider the set of all mappings ...

The exterior of a knot K is the complement of an open solid torus knotted like K. The removed open solid torus is called a tubular neighborhood (Adams 1994, p. 258).

For a connected graph G of graph diameter d, the distance-k graph G_k for k=1, ..., d is a graph with the same vertex set and having edge set consisting of the pairs of ...