order-preserving function
[/ˈɔːrdər prɪˈzɜːrvɪŋ ˈfʌŋkʃən/]
nounpl: order-preserving functions
função que preserva ordem
1. A mathematical function between two ordered sets that maintains the ordering relationship; if x ≤ y in the domain, then f(x) ≤ f(y) in the codomain
The function f(x) = 2x is an order-preserving function from the real numbers to the real numbers.
A função f(x) = 2x é uma função que preserva ordem dos números reais para os números reais.
2. In lattice theory and order theory, a function that respects the partial order structure of the sets involved
In topology, many continuous functions are order-preserving functions between their respective poset structures.
Em topologia, muitas funções contínuas são funções que preservam ordem entre suas respectivas estruturas de ordem parcial.
This is a specialized mathematical term primarily used in academic and research contexts in both Brazil and Portugal. It appears in university-level mathematics curricula, particularly in courses on abstract algebra, order theory, and topology. The term is highly technical and standardized across the Portuguese-speaking mathematical community, with minimal regional variation.
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