Continuity

see also:

• Smoothness

• Curvature

• Critical Points

• Manifolds

• Measure

• Measure Theory

• Topology

• Reimannian Geometry

• Differential Geometry

• Differential Forms

• Continuity Of Splines: https://www.youtube.com/watch?v=jvPPXbo87ds

• Continuity in Metric Spaces: A function between metric spaces is continuous if and only if it preserves the structure of open sets as defined by their metrics. More precisely, a function $f:(X,d_X)\to (Y,d_Y)$ is continuous if the preimage of every open set in $Y$ is an open set in $X$. This definition aligns with the epsilon-delta definition of continuity in metric spaces, highlighting the deep connection between metrics and topology.