THEWAY-BELOW RELATION ON FUNCTION SPACES FROM TOPOLOGICAL SPACE TO DOMAIN

Hadrian Andradi, Dr. Ch. Rini Indrati, M.Si.

2012 | Tesis | S2 Matematika

Relasi way-below pada poset yang kontinu, berdasarkan definisi D.S. Scott, memiliki peranan penting. Relasi tersebut menyatakan aproksimasi suatu elemen dengan menggunakan bagian hingganya. Hal tersebut analog dengan kenyataan bahwa suatu bilangan real dapat dipandang sebagai limit dari barisan bilangan rasional (yang bergerak mendekatinya). Pada tesis ini diberikan karakterisasi relasi way-below pada ruang fungsi dari ruang topologis ke poset kontinu.

The way-below relation on partially ordered sets which are continuous in the sense of D.S. Scott is of paramount importance. The way-below relation expresses the approximation of an element by its finite parts, analogous to the situation where a real number can be perceived as the limit of a sequence of its rational approximants. In this thesis, we present explicit characterizations of the way-below relation on spaces of continuous functions from topological space into continuous poset.

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