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Last seen on: Daily Celebrity Crossword – 4/20/19 Smartypants Saturday
Random information on the term “Net”:
In mathematics, more specifically in general topology and related branches, a net or Moore–Smith sequence is a generalization of the notion of a sequence. In essence, a sequence is a function with domain the natural numbers, and in the context of topology, the codomain of this function is usually any topological space. However, in the context of topology, sequences do not fully encode all information about a function between topological spaces. In particular, the following two conditions are not equivalent in general for a map f between topological spaces X and Y:
It is true, however, that condition 1 implies condition 2. The difficulty encountered when attempting to prove that condition 2 implies condition 1 lies in the fact that topological spaces are, in general, not first-countable.If the first-countability axiom were imposed on the topological spaces in question, the two above conditions would be equivalent. In particular, the two conditions are equivalent for metric spaces.