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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} .
We consider the subfibration of the product variety | | with fiber above the linear system of hyperplanes that intersect X non-transversally at x.. The rank of the fibration in the product is one less than the codimension of , so that the total space has lesser dimension than and so its projection is contained in a divisor of the complete system | |.
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 ...
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.
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 ...
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In differential topology, a branch of mathematics, the Whitney conditions are conditions on a pair of submanifolds of a manifold introduced by Hassler Whitney in 1965.. A stratification of a topological space is a finite filtration by closed subsets F i, such that the difference between successive members F i and F (i − 1) of the filtration is either empty or a smooth submanifold of dimension i.