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A circle-preserving transformation composed of an odd number of inversions.

The inverse function of the logarithm, defined such that log_b(antilog_bz)=z=antilog_b(log_bz). The antilogarithm in base b of z is therefore b^z.

If two quantities A and B are approximately equal, this is written A approx B.

A valuation for which |x|<=1 implies |1+x|<=C for the constant C=1 (independent of x). Such a valuation does not satisfy the strong triangle inequality |x+y|<=max(|x|,|y|).

A group in which any decreasing chain of distinct subgroups terminates after a finite number.

If f is continuous on a closed interval [a,b], then there is at least one number x^* in [a,b] such that int_a^bf(x)dx=f(x^*)(b-a). The average value of the function (f^_) on ...

If O_(p^')(G)=1 and if x is a p-element of G, then L_(p^')(C_G(x))<=E(C_G(x)), where L_(p^') is the p-layer.

The study of map projections and the making of geographical maps.

The underlying set of the fundamental group of X is the set of based homotopy classes from the circle to X, denoted [S^1,X]. For general spaces X and Y, there is no natural ...

Two open manifolds M and M^' are cobordant if there exists a manifold with boundary W^(n+1) such that an acceptable restrictive relationship holds.