1, Research Directions for Machine Learning and Algorithms

2, Resources on Knot theory

3, The Birkhoff-Kakutani theorem

A topological space {X} is said to be metrisable if one can find a metric {d: X \times X \rightarrow [0,+\infty)} on it whose open balls generate the topology.

Theorem 1 (Birkhoff-Kakutani theorem) Let {G} be a topological group (i.e. a topological space that is also a group, such that the group operations {\cdot: G \times G \rightarrow G} and {()^{-1}: G \rightarrow G} are continuous). Then {G} is metrisable if and only if it is both Hausdorff and first countable.