In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n. In this more precise terminology, a manifold is referred to as an n-manifold.
One-dimensional manifolds include lines and circles, but not figure eights (because they have crossing points that are not locally homeomorphic to Euclidean 1-space). Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, which can...
The dollar sign ($ or ) is a symbol primarily used to indicate the various units of currency around the world. The symbol can interchangeably have one or two vertical strokes. In common usage, the sign appears to the left of the amount specified, as in $1 (read: one dollar).
== Origin ==
=== Pillars of Hercules ===
A common hypothesis holds that the sign derives from the symbolic representation of the Pillars of Hercules – this representation can either have a banner separately around each pillar, or as in the Spanish coat of arms, a banner curling between them.
In 1492, Ferdinand II of...
Inspite of knowing a thing or two about limits , this particular question just completely stumps me . What does it want me to do and how do I operate with the modulus ? Taking double derivative of $x^p \sin(\frac{1}{x})+x|x^3|$ also seems too complicated.How do I approach this ?
Test(s) or TEST may refer to:
Test (assessment), an assessment intended to measure the respondents' knowledge or other abilities
List of tests
== Science and technology ==
Experiment, a part of the scientific method
Test method, a definitive procedure that produces a test result
Statistical hypothesis testing, a method of making statistical decisions using experimental data
=== Biology, medicine, and psychology ===
Test (biology), the shell of sea urchins and certain microorganisms
Medical test, to detect, diagnose, or monitor diseases
Psychological testing, the use of behavioral samples to make...
In mathematics, a microbundle is a generalization of the concept of vector bundle, introduced by the American mathematician John Milnor in 1964. It allows the creation of bundle-like objects in situations where they would not ordinarily be thought to exist. For example, the tangent bundle is defined for a smooth manifold but not a topological manifold. Use of microbundles allows the definition of a topological tangent bundle.
== Definition ==
The precise definition of a microbundle follows. Let B be a topological space. Then a n-microbundle consists of a triple (E, i, p) where E is a topological...
