On a problem of spectral posets. (English) Zbl 1049.06002
Summary: In studying the conditions for a poset to be a spectral space, W. J. Lewis and J. Ohm asked in Can. J. Math. 28, 820–835 (1976; Zbl 0313.13003): if the ordered disjoint union of posets \(X_\lambda\) is spectral, are the \(X_\lambda\) also spectral? There is so far no answer to this question in the literature. In this paper, we prove that in certain cases, the answer to this question is affirmative.
MSC:
06A06 | Partial orders, general |
06B30 | Topological lattices |
13A15 | Ideals and multiplicative ideal theory in commutative rings |