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The Klein-Beltrami model of hyperbolic geometry consists of an open disk in the Euclidean plane whose open chords correspond to hyperbolic lines. Two lines l and m are then ...

On a measure space X, the set of square integrable L2-functions is an L^2-space. Taken together with the L2-inner product with respect to a measure mu, <f,g>=int_Xfgdmu (1) ...

For n>=1, let u and v be integers with u>v>0 such that the Euclidean algorithm applied to u and v requires exactly n division steps and such that u is as small as possible ...

A lattice automorphism is a lattice endomorphism that is also a lattice isomorphism.

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. A lattice endomorphism is a mapping h:L->L that preserves both meets and joins.

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. A lattice isomorphism is a one-to-one and onto lattice homomorphism.

Let L=(L, ^ , v ) be a lattice, and let f,g:L->L. Then the pair (f,g) is a polarity of L if and only if f is a decreasing join-endomorphism and g is an increasing ...

Let L=(L, ^ , v ) be a lattice, and let tau subset= L^2. Then tau is a tolerance if and only if it is a reflexive and symmetric sublattice of L^2. Tolerances of lattices, ...

A law is a mathematical statement which always holds true. Whereas "laws" in physics are generally experimental observations backed up by theoretical underpinning, laws in ...

A nonnegative measurable function f is called Lebesgue integrable if its Lebesgue integral intfdmu is finite. An arbitrary measurable function is integrable if f^+ and f^- ...