Some refinements of a selection theorem with O-dimensional domain

• Autorzy: B. Michael
• Języki publikacji: EN

Abstrakty

EN

The following known selection theorem is sharpened, primarily, by weakening the hypothesis that all the sets φ(x) are closed in Y: Let X be paracompact with dimX = 0, let Y be completely metrizable and let φ:X → 𝓕(Y) be l.s.c. Then φ has a selection.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1991-1992
• Tom: 140
• Numer: 3
• Strony: 279-287

Daty

wydano

1992

otrzymano

1991-08-07

Twórcy

autor

B. Michael

• Department of Mathematics, University of Washington, Seattle, Washington 98195, U.S.A.

Bibliografia

• [B] D. Burke, Covering properties, in: Handbook of Set-Theoretic Topology, North-Holland, Amsterdam 1984, 347-422.
• [M1] E. Michael, A note on paracompact spaces, Proc. Amer. Math. Soc. 4 (1953), 831-838.
• [M2] E. Michael, Selected selection theorems, Amer. Math. Monthly 63 (1956), 233-238.
• [M3] E. Michael, Continuous selections I, Ann. of Math. 63 (1956), 361-382.
• [M4] E. Michael, Continuous selections II, Ann. of Math. 64 (1956), 562-580.
• [M5] E. Michael, The product of a normal space and a metric space need not be normal, Bull. Amer. Math. Soc. 69 (1963), 375-376.
• [M6] E. Michael, Continuous selections and countable sets, Fund. Math. 111 (1981), 1-10.
• [M7] E. Michael, A generalization of a theorem on continuous selections, Proc. Amer. Math. Soc. 105 (1989), 236-243.