Artículos con la etiqueta ‘Topología’
Por Camilo Arcaya • 3 mar, 2014 • Category: Filosofía
René Thom ha propuesto el concepto topológico de continuo como respuesta al concepto lógico de infinito. En este trabajo se mostrará que, frente a la definición combinatoria de conjunto infinito propuesta por Cantor, la definición porfiriana de continuo propuesta por Thom salva las paradojas de la teoría de conjuntos y comporta consecuencias ontológicas decisivas en el ámbito del mundo morfológico poniendo límites, por ejemplo, a la evolución ilimitadamente innovadora de Prigogine, etc.
Tags: el continuo, Filosofía, Prigogine, René Thom, Topología
Publicado en Filosofía | No hay comentarios »
Por Camilo Arcaya • 21 jul, 2013 • Category: Crítica
We write the Euler characteristic X(G) of a four dimensional finite simple geometric graph G=(V,E) in terms of the Euler characteristic X(G(w)) of two-dimensional geometric subgraphs G(w). The Euler curvature K(x) of a four dimensional graph satisfying the Gauss-Bonnet relation sum_x K(x) = X(G) can so be rewritten as an average 1-E[K(x,f)]/2 over a collection two dimensional «sectional graph curvatures» K(x,f) through x. Since scalar curvature, the average of all these two dimensional curvatures through a point, is the integrand of the Hilbert action, the integer 2-2 X(G) becomes an integral-geometrically defined Hilbert action functional.
Tags: Discrete Mathematics (cs.DM), Geometría, Geometric Topology (math.GT), matemática discreta, matemáticas, Topología
Publicado en Crítica | No hay comentarios »
Por Camilo Arcaya • 4 jul, 2013 • Category: Opinion
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as well as their applications to real numbers. Various methods to construct topological spaces are presented.
Tags: análisis matemático, Continuidad, Filosofía, Functional Analysis (math.FA), General Topology (math.GN), History and Overview (math.HO), matemáticas, números reales, Topología
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Por Camilo Arcaya • 17 jun, 2013 • Category: Opinion
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. Starting from ZFC, the exposition in this first part includes relation and order theory as well as a construction of number systems.
Tags: conjuntos, Filosofía, fundamentación axiomática, History and Overview (math.HO), Logic (math.LO), Lógica, relaciones, teoría de los números, Topología
Publicado en Opinion | No hay comentarios »
Por Camilo Arcaya • 24 nov, 2012 • Category: Ciencia y tecnología
This is a prejudiced survey on the Ahlfors (extremal) function and the weaker {\it circle maps} (Garabedian-Schiffer’s translation of «Kreisabbildung»), i.e. those (branched) maps effecting the conformal representation upon the disc of a {\it compact bordered Riemann surface}. The theory in question has some well-known intersection with real algebraic geometry, especially Klein’s ortho-symmetric curves via the paradigm of {\it total reality}. This leads to a gallery of pictures quite pleasant to visit of which we have attempted to trace the simplest representatives. This drifted us toward some electrodynamic motions along real circuits of dividing curves perhaps reminiscent of Kepler’s planetary motions along ellipses. The ultimate origin of circle maps is of course to be traced back to Riemann’s Thesis 1851 as well as his 1857 Nachlass. Apart from an abrupt claim by Teichm\»uller 1941 that everything is to be found in Klein (what we failed to assess on printed evidence), the pivotal contribution belongs to Ahlfors 1950 supplying an existence-proof of circle maps, as well as an analysis of an allied function-theoretic extremal problem.
Tags: Complex Variables (math.CV), Geometría, Geometric Topology (math.GT), History and Overview (math.HO), Lógica, matemáticas, Topología, variables complejas
Publicado en Ciencia y tecnología | No hay comentarios »
Por Camilo Arcaya • 12 nov, 2012 • Category: Educacion
In arXiv:1207.0332 [cs.LO] was proposed a graphic lambda calculus formalism, which has sectors corresponding to untyped lambda calculus and emergent algebras. Here we explore the sector covering knot diagrams, which are constructed as macros over the graphic lambda calculus.
Tags: Filosofía, Geometría, Geometric Topology (math.GT), Logic (math.LO), Logic in Computer Science (cs.LO), Lógica, matemáticas, Topología
Publicado en Educacion | No hay comentarios »
Por Camilo Arcaya • 26 oct, 2012 • Category: Opinion
We give a theoretical and applicable framework for dealing with real-world phenomena. Joining pointwise and pointfree notions in BISH, natural topology gives a faithful idea of important concepts and results in intuitionism. Natural topology is well-suited for practical and computational purposes. We give several examples relevant for applied mathematics, such as the decision-support system Hawk-Eye (used in professional tennis), and various real-number representations. We compare CLASS, INT, RUSS, BISH and formal topology. There are links with physics, regarding the topological character of our physical universe.
Tags: Filosofía, frontera, Logic (math.LO), Lógica, matemáticas, Topología
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Por Camilo Arcaya • 23 oct, 2012 • Category: Crítica
We show how changes in unitarity-preserving boundary conditions allow continuous interpolation among the Hilbert spaces of quantum mechanics on topologically distinct manifolds. We present several examples, including a computation of entanglement entropy production. We discuss approximate realization of boundary conditions through appropriate interactions, thus suggesting a route to possible experimental realization. We give a theoretical application to quantization of singular Hamiltonians, and give tangible form to the «many worlds» interpretation of wave functions.
Tags: física cuántica, General Relativity and Quantum Cosmology (gr-qc), High Energy Physics - Theory (hep-th), matemáticas, Quantum Physics (quant-ph), Topología
Publicado en Crítica | No hay comentarios »
Por Camilo Arcaya • 21 sep, 2012 • Category: Opinion
In these expository notes, intended for students without background in point-set topology, we develop the basic theory of the Stone-Cech compactification without reference to open sets, closed sets, filters, or nets. In particular, this means we cannot use any of the usual definitions of topological space. This may seem like proposing to run a marathon while hopping on one foot, but it is easier than it may appear, and not devoid of interest. We use gauge spaces (uniform spaces presented by a family of pseudometrics); we define compactness as total boundedness plus completeness; and we define completeness using a variation on Lawvere’s categorical characterization of completeness for metric spaces.
Tags: Category Theory (math.CT), General Topology (math.GN), infinito matemático, matemáticas, teoría de las categorías, Topología
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Por Camilo Arcaya • 30 jun, 2011 • Category: Opinion
By means of the property of effective local connectivity, the computability of finding the Carath\’eodory extension of a conformal map of a Jordan domain onto the unit disk is demonstrated.
Tags: investigación, Lógica, Topología, variable compleja
Publicado en Opinion | No hay comentarios »