topology

nLab numerable open cover Contents Context Topology topology (point-set topology, point-free topology) see also differential topology, algebraic topology, functional analysis and topological homotopy theory Introduction Basic concepts - open subset, closed subset, neighbourhood - topological space, locale - base for the topology, neighbourhood base - finer/coarser topology - cl…

We propose a three-layered framework for mathematical specialization and research strategy in an era of rapidly advancing artificial intelligence. First, we introduce the "Diffraction Profile," a finite-resource cognitive model that uses a squared-sinc kernel to mathematically describe how deep specialization in a core domain generates non-monotonic, structurally resonant "side lobes" of secondar…

analysis (differential/integral calculus, functional analysis, topology) metric space, normed vector space open ball, open subset, neighbourhood convergence, limit of a sequence compactness, sequential compactness … constructive mathematics, realizability, computability propositions as types, proofs as programs, computational trinitarianism topos, homotopy topos type theory, homotopy type theory …

The Möbius strip is formally identified as the quotient space of the unit square by the equivalence relation $(0,t)\sim(1,1-t)$ (all other points are self-equivalent). In the image above, the band ...

Special and general types Special notions Variants Extra structure Operations Theorems Twisted de Rham cohomology is the twisted cohomology-version of de Rham cohomology, a simple example of twisted differential cohomology. For degree-3 twists this is the codomain of the twisted Chern character on twisted K-theory, and in its orbifold cohomology-generalization it is the codomain of the twisted eq…

analysis (differential/integral calculus, functional analysis, topology) metric space, normed vector space open ball, open subset, neighbourhood convergence, limit of a sequence compactness, sequential compactness … constructive mathematics, realizability, computability propositions as types, proofs as programs, computational trinitarianism topos, homotopy topos type theory, homotopy type theory …

This volume reconstructs the Pulickal research programme across computational algorithms, phase based operators, topology, information, hardware, stochastic systems, and applications. It develops precise mathematical models, verifies results, identifies limitations, and defines testable research problems linking theory with computation and experiment. ( direct link )

Hand-hatched surfaces after the mid-century manner of Francis, Apéry, Hilbert–Cohn-Vossen. Drag to turn the model freely (shift-drag to roll it); scroll to approach. The drawing is made of strokes, not pixels. Silhouettes are the zero set of n·v on the mesh (found with interpolated normals, so they chain into smooth curves), boundaries and the double curve of an immersion are added as further cha…

The five Platonic solids are the epitome of perfection—at least in mathematics. Topology explains why there are only five of them

nLab topological K-theory Context Cohomology cohomology Special and general types Special notions Variants Extra structure Operations Theorems Topology topology (point-set topology, point-free topology) see also differential topology, algebraic topology, functional analysis and topological homotopy theory Introduction Basic concepts - open subset, closed subset, neighbourhood - t…

I am looking for references on the theory of homogeneous spaces $G/H$, where $G$ is a totally disconnected locally compact (tdlc) group and $H\leq G$ is a closed subgroup. My motivation comes from the ...

Special and general types Special notions Variants Extra structure Operations Theorems This page is to record the reference: John Frank Adams: Stable homotopy and generalized homology Chicago Lectures in Mathematics University of Chicago Press (1974) ISBN:978-0-226-00524-9 ucp:bo21302708 on stable homotopy theory and generalised homology theory, with emphasis on complex cobordism theory, complex …

It is possible to use various methods to assign finite values to divergent series (e.g., regularization, analytic continuation). See, for instance, this or this Q&As here on MSE. The limits of ...