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2. Calcite - Wikipedia

   en.wikipedia.org/wiki/Calcite

   Calcite is a carbonate mineral and the most stable polymorph of calcium carbonate (CaCO 3). It is a very common mineral, particularly as a component of limestone. Calcite defines hardness 3 on the Mohs scale of mineral hardness, based on scratch hardness comparison. Large calcite crystals are used in optical equipment, and limestone composed ...

3. Marble - Wikipedia

   en.wikipedia.org/wiki/Marble

   Marble is a metamorphic rock consisting of carbonate minerals (most commonly calcite (CaCO 3) or dolomite (CaMg (CO 3) 2) that have recrystallized under the influence of heat and pressure. [1] It has a crystalline texture, and is typically not foliated (layered), although there are exceptions. In geology, the term marble refers to metamorphosed ...

4. Haar measure - Wikipedia

   en.wikipedia.org/wiki/Haar_measure

   In mathematical analysis, the Haar measure assigns an "invariant volume" to subsets of locally compact topological groups, consequently defining an integral for functions on those groups. This measure was introduced by Alfréd Haar in 1933, though its special case for Lie groups had been introduced by Adolf Hurwitz in 1897 under the name ...

5. Quartz - Wikipedia

   en.wikipedia.org/wiki/Quartz

   Quartz is a hard, crystalline mineral composed of silica (silicon dioxide). The atoms are linked in a continuous framework of SiO 4 silicon–oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical formula of SiO 2. Quartz is, therefore, classified structurally as a framework silicate mineral and ...

6. Group algebra of a locally compact group - Wikipedia

   en.wikipedia.org/wiki/Group_algebra_of_a_locally...

   If G is a locally compact Hausdorff group, G carries an essentially unique left-invariant countably additive Borel measure μ called a Haar measure.Using the Haar measure, one can define a convolution operation on the space C c (G) of complex-valued continuous functions on G with compact support; C c (G) can then be given any of various norms and the completion will be a group algebra.

7. Classification of manifolds - Wikipedia

   en.wikipedia.org/wiki/Classification_of_manifolds

   There is a unique connected 0-dimensional manifold, namely the point, and disconnected 0-dimensional manifolds are just discrete sets, classified by cardinality. They have no geometry, and their study is combinatorics. A connected compact 1-dimensional manifold without boundary is homeomorphic (or diffeomorphic if it is smooth) to the circle.