In algebraic topology, in the cellular approximation theorem, a map between CW-complexes can always be taken to be of a specific type.
 Concretely, if "X" and "Y" are CW-complexes, and "f" : "X" → "Y" is a continuous map, then "f" is said to be "cellular", if "f" takes the "n"-skeleton of "X" to the "n"-skeleton of "Y" for all "n", i.e. if formula_1 for all "n".
 The content of the cellular approximation theorem is then that any continuous map "f" : "X" → "Y" between CW-complexes "X" and "Y" is homotopic to a cellular map, and if "f" is already cellular on a subcomplex "A" of "X", then we can furthermore choose the homotopy to be stationary on "A".
 From an algebraic topological viewpoint, any map between CW-complexes can thus be taken to be cellular.
In differential topology, the transversality theorem, also known as the Thom Transversality Theorem, is a major result that describes the transverse intersection properties of a smooth family of smooth maps.
 It says that transversality is a generic property: any smooth map formula_1, may be deformed by an arbitrary small amount into a map that is transverse to a given submanifold formula_2.
 Together with the Pontryagin-Thom construction, it is the technical heart of cobordism theory, and the starting point for surgery theory.
 The finite-dimensional version of the transversality theorem is also a very useful tool for establishing the genericity of a property which is dependent on a finite number of real parameters and which is expressible using a system of nonlinear equations.
 This can be extended to an infinite-dimensional parametrization using the infinite-dimensional version of the transversality theorem.
Skelton was born on February 9, 1886, his family living in Edgerton, Ohio, at the time.
 His parents were James G. Skelton and Sophia Skelton.
 James was a shopkeeper selling horse harness and saddlery, and the future automotive engineer worked as a shop apprentice in his youth.
 Eschewing horses, he graduated from Ohio State University with a degree in mechanical engineering.
In the mathematical discipline of graph theory, the Erdős–Pósa theorem, named after Paul Erdős and Lajos Pósa, states that there is a function "f"("k") such that for each positive integer k , every graph either contains k vertex-disjoint circuits or it has a feedback vertex set of "f"("k") vertices that intersects every circuit.
 Furthermore, "f"("k") = O("k" log "k") in the sense of Big O notation.
 Because of this theorem, circuits are said to "have the Erdős–Pósa property".
In mathematics, specifically in the study of vector bundles over complex Kähler manifolds, the Nakano vanishing theorem, sometimes called the Akizuki–Nakano vanishing theorem, generalizes the Kodaira vanishing theorem.
 Given a compact complex manifold "M" with a holomorphic line bundle "F" over "M", the Nakano vanishing theorem provides a condition on when the cohomology groups formula_1 equal zero.
 Here, formula_2 denotes the sheaf of holomorphic ("p",0)-forms taking values on "F".
 The theorem states that, if the first Chern class of "F" is negative,formula_3Alternatively, if the first Chern class of "F" is positive,formula_4
Rouché's theorem, named after Eugène Rouché, states that for any two complex-valued functions "f" and "g" holomorphic inside some region "K" with closed contour formula_1, if |"g"("z")| < |"f"("z")| on formula_1, then "f" and "f" + "g" have the same number of zeros inside "K", where each zero is counted as many times as its multiplicity.
 This theorem assumes that the contour formula_1 is simple, that is, without self-intersections.
 Rouché's theorem is an easy consequence of a stronger symmetric Rouché's theorem described below.
In mathematical economics, Topkis's theorem is a result that is useful for establishing comparative statics.
 The theorem allows researchers to understand how the optimal value for a choice variable changes when a feature of the environment changes.
 The result states that if "f" is supermodular in ("x","θ"), and "D" is a lattice, then formula_1 is nondecreasing in "θ".
 The result is especially helpful for establishing comparative static results when the objective function is not differentiable.
Robert Jackson Marks II is a polymath electrical engineer.
 His contributions include the Zhao-Atlas-Marks (ZAM) time-frequency distribution in the field of signal processing, the Cheung–Marks theorem in Shannon sampling theory and the Papoulis-Marks-Cheung (PMC) approach in multidimensional sampling.
 He was instrumental in the defining of the field of computational intelligence and co-edited the first book using "computational intelligence" in the title.
 A Christian and an old earth creationist, he is a subject of the 2008 pro-intelligent design motion picture, .
In information theory, the Cheung–Marks theorem, named after K. F. Cheung and Robert J. Marks II, specifies conditions where restoration of a signal by the sampling theorem can become ill-posed.
 It offers conditions whereby "reconstruction error with unbounded variance [results] when a bounded variance noise is added to the samples."
In physics, the no-deleting theorem of quantum information theory is a no-go theorem which states that, in general, given two copies of some arbitrary quantum state, it is impossible to delete one of the copies.
 It is a time-reversed dual to the no-cloning theorem, which states that arbitrary states cannot be copied.
 This theorem seems remarkable, because, in many senses, quantum states are fragile; the theorem asserts that, in a particular case, they are also robust.
 Physicist Arun K. Pati along with Samuel L. Braunstein proved this theorem.

Question: What type of engineer worked with K.F Cheung in establishing the Cheung-Marks theorem?
Answer: polymath electrical engineer