Mathematical structures

thumb|upright=1.5|A three-dimensional model of a Figure-eight knot (mathematics)|figure-eight knot. The figure-eight knot is a [[prime knot and has an Alexander–Briggs notation of 41.]]

the basic algebraic structure of linear algebra; a module over a field, such that its elements can be added together or scaled by elements of the field

thumb|Sierpiński carpet|Sierpiński Carpet - Infinite perimeter and zero area thumb|Highly magnified area on the boundary of the Mandelbrot set thumb|The Mandelbrot set: its boundary is a fractal curve with [[Hausdorff dimension 2. (Note that the colored sections of the image are not actually part of the Mandelbrot Set, but rather they are based on how quickly the function that produces it diverges.)|200x200px]] thumb|Mandelbrot set with 12 encirclements

set equipped with a metric (distance function)

set equipped with one or more finitary operations defined on it

combination of a set and an extra structure on it; more precisely, an object of a concrete category

frame|An example of an undirected hypergraph, with X = \{v_1, v_2, v_3, v_4, v_5, v_6, v_7\} and E = \{e_1,e_2,e_3,e_4\} = \{\{v_1, v_2, v_3\}, \{v_2,v_3\}, \{v_3,v_5,v_6\}, \{v_4\}\}. This hypergraph has order 7 and size 4. Here, edges do not just connect two vertices but several, and are represented by colors. alt=PAOH visualization of a hypergraph|thumb|Alternative representation of the hypergraph reported in the figure above, called PAOH. Edges are vertical lines connecting vertices. V7 is an isolated vertex. Vertices are aligned to the left. The legend on the right shows the names of the

set together with an interpretation of a given first-order language

mathematical structure

a topological group that is isomorphic to the inverse limit of an inverse system of solvable groups