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Given the determinants of chemical bonding and the chemical properties of the atoms, topology provides a model for explaining how the atoms ethereal wave functions must fit together. Molecular topology is a part of mathematical chemistry dealing with the algebraic description of chemical compounds so allowing a unique and easy characterization ...
For example, the Euclidean topology on the plane admits as a base the set of all open rectangles with horizontal and vertical sides, and a nonempty intersection of two such basic open sets is also a basic open set. But another base for the same topology is the collection of all open disks; and here the full (B2) condition is necessary.
A typical example is a surface such as the one depicted at the right. Moreover, is a point in X called the base-point. (As is explained below, its role is rather auxiliary.) The idea of the definition of the homotopy group is to measure how many (broadly speaking) curves on X can be deformed into each other. The precise definition depends on ...
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
Base (topology) – Collection of open sets used to define a topology; Filter (set theory) – Family of sets representing "large" sets; Filters in topology – Use of filters to describe and characterize all basic topological notions and results. Locally convex topological vector space – Vector space with a topology defined by convex open sets
A strong base is a basic chemical compound that can remove a proton (H +) from (or deprotonate) a molecule of even a very weak acid (such as water) in an acid–base reaction. Common examples of strong bases include hydroxides of alkali metals and alkaline earth metals, like NaOH and Ca(OH) 2, respectively. Due to their low solubility, some ...
Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. Topological indices are used for example in the development of quantitative structure-activity relationships (QSARs) in which the biological activity or other properties of molecules are correlated with their chemical ...
The non-chiral Su–Schrieffer–Heeger model (=), can be associated with symmetry class BDI with an integer topological invariant due to gauge invariance. [6] [7] The problem is similar to the integer quantum Hall effect and the quantum anomalous Hall effect (both in =) which are A class, with integer Chern number.