In mathematics, in the field of potential theory, the fine topology is a natural topology for setting the study of subharmonic functions. In the earliest...

mathematics, fine topology can refer to: Fine topology (potential theory) The sense opposite to coarse topology, namely: A term in comparison of topologies which...

functions continuous. Fine topology (potential theory) On Euclidean space R n {\displaystyle \mathbb {R} ^{n}} , the coarsest topology making all subharmonic...

defined in the article Fine topology (potential theory). The set S {\displaystyle S} is not closed in the euclidean topology since it does not contain...

A theory of everything (TOE), final theory, ultimate theory, unified field theory, or master theory is a hypothetical singular, all-encompassing, coherent...

with a projection, it follows that the ideles carry a finer topology than the subspace topology from A. Inside AN, the product KN lies as a discrete subgroup...

topologies are used in other branches of mathematics; for example, the Zariski topology, which is fundamental in algebraic geometry and scheme theory...

Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f...

its origins in 19th century group theory where a subset of a group was called a complex.) Alexandrov topology – topology in which the intersection of any...

Quantum mechanics is the fundamental physical theory that describes the behavior of matter and of light; its unusual characteristics typically occur at...

distribution) the chromatic number of a graph in graph theory the Euler characteristic in algebraic topology electronegativity in the periodic table the Fourier...

{\displaystyle X'} such that the norm induced topology on X ′ {\displaystyle X'} is finer than the weak-* topology. Consequently, if a Fréchet space is not...

In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines field theory and the principle of relativity with ideas behind...

extensively in partial differential equations, complex analysis and potential theory. Intuitively, subharmonic functions are related to convex functions...

Makarov works in complex analysis and related fields (potential theory, harmonic analysis, spectral theory) as well as on various applications to complex dynamics...

American mathematician who worked mainly in the areas of geometric topology and continuum theory. His father was named Rupert Henry, but Bing's mother thought...

according to the coordinates of biological drive economy, dynamics and topology). He discovered that the instinctive impulses are expressed most clearly...

Probability theory Measure theory Integral geometry Ergodic theory Stochastic process Geometry (outline) and Topology General topology Algebraic topology Geometric...

contributions, in general topology he introduced the notions of filter and ultrafilter and in potential theory he developed the fine topology and proved Cartan's...

"Geometric Aspects in the Development of Knot Theory" (PDF). In James, I.M. (ed.). History of Topology. Amsterdam: Elseviwer. pp. 301–357. Lisitsa, Alexei;...

drastic effect on the topological structure underlying the solution. The topology of each stage of an iterative solution in the transportation problem is...

Barabási and Réka Albert at the University of Notre Dame who mapped the topology of a portion of the World Wide Web, finding that some nodes, which they...

important role in both quantum field theory and differential geometry. This was, however, gradually supplemented by topology and functional analysis in the...

calculus, linear algebra, set theory, and topology as well as branches of mathematical analysis such as real analysis, measure theory, Fourier analysis, and...

J. (1999). "5. Differential Forms". In James, I. M. (ed.). History of Topology. Amsterdam: Elsevier. pp. 111–122. ISBN 9780444823755. See: Katz, Victor...

Lehoucq, Roland; Uzan, Jean-Philippe (October 9, 2003). "Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic...

abundance of compact sets in relation to the causal structure. Since finer topologies have less compact sets we can also say that the balance is on the number...

coupling results in discrete minima. The high symmetry of the double-cone topology of the linear E ⊗ e JT system directly reflects the high underlying symmetry...

ISBN 978-0471631170. Bott, R. (1956). "An application of the Morse theory to the topology of Lie-groups". Bulletin de la Société Mathématique de France. 84:...

inflationary theory. However, some physicists deny that inflationary theory resolves the flatness problem, arguing that it merely moves the fine-tuning from...