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A space is an absolute neighborhood retract for the class , written (), if is in and whenever is a closed subset of a space in , is a neighborhood retract of . Various classes C {\displaystyle {\mathcal {C}}} such as normal spaces have been considered in this definition, but the class M {\displaystyle {\mathcal {M}}} of metrizable spaces ...
Karol Borsuk (8 May 1905 – 24 January 1982) was a Polish mathematician. His main area of interest was topology . He made significant contributions to shape theory , a term which he coined.
The concept in topology was defined by Karol Borsuk in 1931. [ 2 ] Borsuk's student, Samuel Eilenberg , was with Saunders Mac Lane the founder of category theory, and (as the earliest publications on category theory concerned various topological spaces) one might have expected this term to have initially be used.
Systems analysis is "the process of studying a procedure or business to identify its goal and purposes and create systems and procedures that will efficiently achieve them". Another view sees systems analysis as a problem-solving technique that breaks a system down into its component pieces and analyses how well those parts work and interact to ...
The Borsuk–Ulam theorem has several equivalent statements in terms of odd functions. Recall that S n {\displaystyle S^{n}} is the n -sphere and B n {\displaystyle B^{n}} is the n -ball : If g : S n → R n {\displaystyle g:S^{n}\to \mathbb {R} ^{n}} is a continuous odd function, then there exists an x ∈ S n {\displaystyle x\in S^{n}} such ...
Shape theory is a branch of topology that provides a more global view of the topological spaces than homotopy theory. The two coincide on compacta dominated homotopically by finite polyhedra . Shape theory associates with the Čech homology theory while homotopy theory associates with the singular homology theory.
In mathematics, the Bing–Borsuk conjecture states that every -dimensional homogeneous absolute neighborhood retract space is a topological manifold. The conjecture has been proved for dimensions 1 and 2, and it is known that the 3-dimensional version of the conjecture implies the Poincaré conjecture .
Constructing the nerve of an open good cover containing 3 sets in the plane.. In topology, the nerve complex of a set family is an abstract complex that records the pattern of intersections between the sets in the family.