For a Hausdorff topologized semilattice ▫$X$▫ its ▫$Lawson \; number$▫ ▫$\bar\Lambda(X)$▫ is the smallest cardinal ▫$\kappa$▫ such that for any distinct points ▫$x,y\in X$▫ there exists a family ...▫$\mathcal U$▫ of closed neighborhoods of ▫$x$▫ in ▫$X$▫ such that ▫$|\mathcal U|\le\kappa$▫ and ▫$\bigcap\mathcal U$▫ is a subsemilattice of ▫$X$▫ that does not contain ▫$y$▫. It follows that ▫$\bar\Lambda(X) \le \bar\psi(X)$▫, where ▫$\bar\psi(X)$▫ is the smallest cardinal ▫$\kappa$▫ such that for any point ▫$x\in X$▫ there exists a family ▫$\mathcal U$▫ of closed neighborhoods of ▫$x$▫ in ▫$X$▫ such that ▫$|\mathcal U|\le\kappa$▫ and ▫$\bigcap\mathcal U=\{x\}$▫. We prove that a compact Hausdorff semitopological semilattice ▫$X$▫ is Lawson (i.e., has a base of the topology consisting of subsemilattices) if and only if ▫$\bar\Lambda(X)=1$▫. Each Hausdorff topological semilattice ▫$X$▫ has Lawson number ▫$\bar\Lambda(X)\le\omega$▫. On the other hand, for any infinite cardinal ▫$\lambda$▫ we construct a Hausdorff zero-dimensional semitopological semilattice ▫$X$▫ such that ▫$|X|=\lambda$▫ and ▫$\bar\Lambda(X)=\bar\psi(X)=cf(\lambda)$▫. A topologized semilattice ▫$X$▫ is called (i) ▫$\omega$▫-▫$Lawson$▫ if ▫$\bar\Lambda(X) \le \omega$▫; (ii) ▫$complete$▫ if each non-empty chain ▫$C\subset X$▫ has ▫$\inf C\in\overline{C}$▫ and ▫$\sup C\in\overline{C}$▫. We prove that for any complete subsemilattice ▫$X$▫ of an ▫$\omega$▫-Lawson semitopological semilattice ▫$Y$▫, the partial order ▫$\le_X=\{(x,y)\in X\times X:xy=x\}$▫ of ▫$X$▫ is closed in ▫$Y\times Y$▫ and hence ▫$X$▫ is closed in ▫$Y$▫. This implies that for any continuous homomorphism ▫$h:X\to Y$▫ from a compete topologized semilattice ▫$X$▫ to an ▫$\omega$▫-Lawson semitopological semilattice ▫$Y$▫ the image ▫$h(X)$▫ is closed in ▫$Y$▫.
Bibliografsko gradivo je bilo uspešno dodano na polico.
Dodajanje bibliografskega gradiva na polico ni uspelo.
Gradivo je že na polici.
Trajna povezava
URL:
Faktor vpliva
Dostop do baze podatkov JCR je dovoljen samo uporabnikom iz Slovenije. Vaš trenutni IP-naslov ni na seznamu dovoljenih za dostop, zato je potrebna avtentikacija z ustreznim računom AAI.
Leto
Faktor vpliva
Izdaja
Kategorija
Razvrstitev
JCR
SNIP
JCR
SNIP
JCR
SNIP
JCR
SNIP
Izberite knjižnično izkaznico:
Baze podatkov,
v katerih je revija indeksirana
Ime baze podatkov
Področje
Leto
Povezave do osebnih bibliografij avtorjev
Povezave do podatkov o raziskovalcih v sistemu SICRIS
Storitev za pridobivanje naslova trenutno ni dostopna, prosimo, poskusite še enkrat.
S klikom na gumb "V redu" boste potrdili zgoraj izbrano prevzemno mesto in dokončali postopek rezervacije.
S klikom na gumb "V redu" boste potrdili zgoraj izbrano prevzemno mesto in naslov za dostavo ter dokončali postopek rezervacije.
S klikom na gumb "V redu" boste potrdili zgoraj izbrani naslov za dostavo in dokončali postopek rezervacije.
Obvestilo
Trenutno je storitev za avtomatsko prijavo in rezervacijo nedostopna. Gradivo lahko rezervirate sami na portalu Biblos ali ponovno poskusite tukaj kasneje.
Citiranje
Funkcionalnost trenutno ni na voljo. Prosimo, poskusite kasneje.
PDF
