For more information about countable and uncountable sets, see books about "Analysis" (as advanced calculus is called). For example, Introductory Real Analysis, by A.N. Kolmogorov and S.V. Fomin (see ...
Every continuous function from a countable compact linearly ordered set $A$ into a Banach space $V$ (vanishing at the least element of $A$) admits a representation as ...
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