Īlthough the equivalence between (i) and (iii) in the theorem depends on Alexander-Pontryagin duality, this note, in spirit, belongs to the so called Shape Theory introduced by K. The correct symbol for the number four is, not.
We now answer the first question in our title:ĬOROLLARY. A number in S (other than 1 ) is prime if and only if it has trivial homotopy type at equivalently, it does not tear the sheet in separate pieces. Ī and b cut a sheet in the same number of pieces if you write them down with a scalpel.ĬOROLLARY.For a, b ∈ S the following are equivalent:Ī and b have the same number of proper prime divisors (counted with multiplicities). Given a number n, a proper prime divisor of n is a prime number, different from n, that divides n evenly. Let us use the word number for both the concept and the numeral. Readers may be unaware of the relationship between divisibility properties of numbers and topological properties of the numerals used to represent them. Depertmento de Matemática Aplicada a los Recursos Natureles
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