Connectedness in Topology
A topological space is said to be connected if it is not the union of two disjoint nonempty open sets. A set is open if it contains no point lying on its boundary; thus, in an informal, intuitive sense, the fact that a space can be partitioned into disjoint open sets suggests that the boundary between the two sets is not part of the space, and thus splits it into two separate pieces.
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“Kids are fascinated by stories about what they were like when they were babies and what they said and did as they grew. This sense of history and connectedness increases your children’s feelings of security and safety, and helps them build the ability to make healthy connections in the world at large.”
—Stephanie Martson (20th century)