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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.
[7] For all n for fields of revolution — shown by Boris Dekster (1995). [8] The problem was finally solved in 1993 by Jeff Kahn and Gil Kalai, who showed that the general answer to Borsuk's question is no. [9] They claim that their construction shows that n + 1 pieces do not suffice for n = 1325 and for each n > 2014.
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 .
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 ...
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.
Structural balance theory posits that some types of triads are forbidden and others are permitted on the basis of four rules. [4]Using the term “friend” to designate a positive sentiment and the term “enemy” to designate a negative sentiment, the classic balance model defines a sentiment network as balanced if it contains no violations of four assumptions:
The Borsuk–Ulam theorem is equivalent to the following statement: A continuous odd function from an n-sphere into Euclidean n-space has a zero. PROOF: PROOF: If the theorem is correct, then it is specifically correct for odd functions, and for an odd function, g ( − x ) = g ( x ) {\displaystyle g(-x)=g(x)} iff g ( x ) = 0 {\displaystyle g(x ...
Spiral Dynamics describes how value systems and worldviews emerge from the interaction of "life conditions" and the mind's capacities. [8] The emphasis on life conditions as essential to the progression through value systems is unusual among similar theories, and leads to the view that no level is inherently positive or negative, but rather is a response to the local environment, social ...