We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
A short proof is given of an internal characterization of completely regular spaces due to J. Kerstan.
1.Alexandroff, A. D., Additive set functions in abstract spaces, Math. Sbornik 50, (1940), 307-348; 51 (1941), 563-628; 55, (1943) 169-238.Google Scholar
2
2.Frink, O., Compactifications and semi-normal spaces, Amer. J. Math.86, (1964), 602-607.CrossRefGoogle Scholar
3
3.Gillman, L. and Jerison, M., Rings of continuous functions, Van Nostrand Reinhold Company, New York et al, 1960.10.1007/978-1-4615-7819-2CrossRefGoogle Scholar
4
4.deGroot, J. and Aarts, J. M., Complete regularity as a separation axiom, Canad. J. Math.21, (1969), 96-105.CrossRefGoogle Scholar
5
5.Hamburger, P., Complete regularity as a separation axiom, Periodica Math. Hungar. 4, 39-44 (1973).10.1007/BF02018035CrossRefGoogle Scholar
6
6.Johnson, D. G. and Mandelker, M., Separating chains in topological spaces, J. London Math. Soc. (2) 4 (1971/72), 510-512.Google Scholar
7
7.Kerstan, J., Eine Charakterisierung der vollstàndig regulàren Raurne, Math. Nachrichten17 (1958), 27-46.10.1002/mana.19580170107CrossRefGoogle Scholar
8
8.Reynolds, G., Alexandroff algebras and complete regularity, Proc. Amer. Math. Soc.76 (1979), 322-326.10.1090/S0002-9939-1979-0537098-5CrossRefGoogle Scholar
9
9.Steiner, E. F., Normal families and completely regular spaces, Duke Math. J.33 (1966), 743-746.10.1215/S0012-7094-66-03389-8CrossRefGoogle Scholar
10
10.Zaicev, V. I., On the theory of Tychonoff spaces, Vest. Mosc. Univ. Math. Mech. (1967), 48-57.Google Scholar