Edge loops (Ctrl+R) create crisp edges and additional geometry. Inset (I) creates windows around selected faces. Extrude (E) allows shape modification of additional geometry. Vertex/Edge Slide (G twice) moves vertices along edges
Inverted normals can be fixed by pressing Shift+N in edit mode. Zero-area faces can be detected using the center checkbox in the overlay menu. Unconnected edges can be merged using the M key with "by distance". Loose geometry can be removed using the L key and Ctrl+I
A norm is a function from vector spaces to non-negative real numbers. Norms must satisfy triangle inequality, absolute homogeneity, and positive definiteness. Every norm is a seminorm, which is also a sublinear function
Compactness extends closed and bounded subsets of Euclidean space. A compact space contains all limiting values of points. The unit interval [0,1] is compact, while open intervals are not. The entire space itself is not compact
Born in Nancy in 1854 into an influential French family. Excelling student at Lycée Nancy, graduating in 1871. Graduated from École Polytechnique in 1875 and École des Mines in 1879
Dimension is the minimum number of coordinates needed to specify a point. A line has dimension 1, a surface 2, and a cube 3. Dimension is an intrinsic property independent of space dimension