C[sub p](X) is not G[sub delta, sigma] : a simple proof

• Autorzy: Mill J.
• Języki publikacji: EN

Abstrakty

EN

It is known that if C[sub p](X) is a G[sub delta, sigma]-subset of R[sup x] then X is discrete. We present a simple proof of this.

Słowa kluczowe

EN

function space; G[sub delta, sigma]-subset

PL

topologia

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1999
• Tom: Vol. 47, no 4
• Strony: 319--323
• Opis fizyczny: Bibliogr. 6 poz.,

Twórcy

autor

Mill J.

• Faculteit Der Exacte Wetenschappen, Divisie Wiskunde En Informatica, Vrije Universiteit, De Boelelaan 1081a, 1081 Hv Amsterdam, The Netherlands

Bibliografia

• [1] R. Cauty, T. Dobrowolski, W. Marciszewski, A contribution to the topological classification of the spaces C p (X), Fund. Math., 142 (1993) 269-301.
• [2] J. Dijkstra, T. Grilliot, D. J. Lutzer, J. van Mill, Function spaces of low Borel complexity, Proc. Amer. Math. Soc., 94 (1985) 703-710.
• [3] T. Dobrowolski, S.P. Gulko, J. Mogilski, Function spaces homeomorphic to the countable product of I", Top. Appl., 34 (1990) 153-160.
• [4] A. J. M. van Engelen, Homogeneous zero-dimensional absolute Bored sets, CWI Tract, vol. 27, Centre for Mathematics and Computer Science, Amsterdam 1986.
• [5] D. J. Lutzer, R. McCoy, Category in function spaces. I, Pac. J. Math. 90 (1980), 145-168.
• [6] J. van Mill, Infinite-dimensional topology: prerequisites and introduction, North-Holland Publishing Company, Amsterdam 1989.