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In mathematics, transversality is a notion that describes how spaces can intersect; transversality can be seen as the "opposite" of tangency, and plays a role in general position. It formalizes the idea of a generic intersection in differential topology. It is defined by considering the linearizations of the intersecting spaces at the points of ...
An important result about transversality states that if a smooth map is transverse to , then () is a regular submanifold of . If X {\displaystyle X} is a manifold with boundary , then we can define the restriction of the map f {\displaystyle f} to the boundary, as ∂ f : ∂ X → Y {\displaystyle \partial f\colon \partial X\rightarrow Y} .
The 2025 CBSE board examination for Class 10 were held from 15 February till 18 March and from 15 February till 4 April for class 12. The usual starting time for each exam was 10:30 am( IST ) but depending on the length and/or maximum marks for the subject, the finishing time was either 12:30 pm ( IST ) (2 hours, shorter exams, usually 40-50 ...
In mathematics, the theorem of Bertini is an existence and genericity theorem for smooth connected hyperplane sections for smooth projective varieties over algebraically closed fields, introduced by Eugenio Bertini.
All India Secondary School Examination, commonly known as the class 10th board exam, is a centralized public examination that students in schools affiliated with the Central Board of Secondary Education, primarily in India but also in other Indian-patterned schools affiliated to the CBSE across the world, taken at the end of class 10. The board ...
A fundamental question in the study of SDR is whether or not an SDR exists. Hall's marriage theorem gives necessary and sufficient conditions for a finite collection of sets, some possibly overlapping, to have a transversal. The condition is that, for every integer k, every collection of k sets must contain in common at least k different elements.
The proof depends on and is intimately related to the transversality properties of smooth manifolds—see Thom transversality theorem. By reversing this construction, John Milnor and Sergei Novikov (among many others) were able to answer questions about the existence and uniqueness of high-dimensional manifolds: this is now known as surgery theory.
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