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A topological transformation in which a surface is made out of an infinitely elastic material which, however, may not be torn or cut. Using this simple prescription gives the ...

A property that is always fulfilled by the product of topological spaces, if it is fulfilled by each single factor. Examples of productive properties are connectedness, and ...

The term rectification is sometimes used to refer to the determination of the length of a curve. Rectification also refers to the operation which converts the midpoints of ...

In the 1930s, Reidemeister first rigorously proved that knots exist which are distinct from the unknot. He did this by showing that all knot deformations can be reduced to a ...

The vector space tensor product V tensor W of two group representations of a group G is also a representation of G. An element g of G acts on a basis element v tensor w by ...

Given a map f:S->T between sets S and T, the map g:T->S is called a right inverse to f provided that f degreesg=id_T, that is, composing f with g from the right gives the ...

The set difference A\B is defined by A\B={x:x in A and x not in B}. Here, the backslash symbol is defined as Unicode U+2216. The set difference is therefore equivalent to the ...

Shephard's conjecture states that every convex polyhedron admits a self-unoverlapping unfolding (Shephard 1975). This question is still unsettled (Malkevitch), though most ...

The Steenrod algebra has to do with the cohomology operations in singular cohomology with integer mod 2 coefficients. For every n in Z and i in {0,1,2,3,...} there are ...

In the process of attaching a k-handle to a manifold M, the boundary of M is modified by a process called (k-1)-surgery. Surgery consists of the removal of a tubular ...