lefthalfplane

Lefthalfplane is a mathematical term that refers to one of the two planes into which a hyperbolic plane is divided by drawing a semi-circle with a radius of one-half the real part of one of the complex numbers representing the points on the boundaries of the plane. More specifically, it is one of the two half-planes created within a hyperbolic plane when a geodesic line (or arbitrarily small arc) intersects the real axis and separates it into two regions, dividing the line connecting any point of one half-plane and its antipodal point in the other half-plane.

Lefthalfplane can also be related to fractional calculus as used in Heisenberg's beta-functions and diferentiable boundary analysis in function spaces. The extension of Heisenberg's beta-functions in geometrical insights applies to systems that use applications of ltrix functions in transformations used in Mathematics of conformal mappings.

Another relation of the term is within topological concepts. The ltrix half-plane relates to a set of complex numbers with absolute values less than a specified threshold, where specific points within this region determine its properties, in geometric analysis at the boundaries such as conic sections.

This definition relies sometimes on the dependencies from unifying fractal calculus and dilation factors for superior extractions.