Previous |  Up |  Next


function spaces; pointwise topology; uniform homeomorphisms; ordinal numbers
We give a partial classification of spaces $C_p([1,\alpha])$ of continuous real valued functions on ordinals with the topology of pointwise convergence with respect to homeomorphisms and uniform homeomorphisms.
[1] Arkhangel'skii A.V.: Topological Function Spaces. Kluwer Academic Publishers, Dordrecht, 1992. MR 1144519
[2] Baars J., de Groot J.: On topological and linear equivalence of certain function spaces. CWI Tract 86, Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, Amsterdam, 1992. MR 1182148 | Zbl 0755.54007
[3] Gul'ko S.P.: The space $C_p(X)$ for countable infinite compact $X$ is uniformly homeomorphic to $c_0$. Bull. Polish Acad. Sci. Math. 36 (1988), 391-396. MR 1101684
[4] Gul'ko S.P.: Spaces of continuous functions on ordinals and ultrafilters. Mat. Zametki 47 (1990), 26-34. MR 1057084
[5] Kislyakov S.V.: Classification of spaces of continuous functions of ordinals. Siberian Math. J. 16 (1975), 226-231. Zbl 0327.46033
Partner of
EuDML logo