On paracompact spaces and projectively inductively closed functors
Submitted: 2014-01-27
|Accepted: 2014-01-27
|Published: 2002-04-01
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Keywords:
Stratifiable space, Paracompact σ-spaces, Paracompact Σ-spaces, Paracompact p-space, Projectively inductively closed functor
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Abstract:
In this paper we introduce a notion of projectively inductively closed functor (p.i.c.-functor). We give sufficient conditions for a functor to be a p.i.c.-functor. In particular, any finitary normal functor is a p.i.c.-functor. We prove that every preserving weight p.i.c.- functor of a finite degree preserves the class of stratifiable spaces and the class of paracompact -spaces. The same is true (even if we omit a preservation of weight) for paracompact -spaces and paracompact p-spaces.
References:
Yu. Al'-Kassas, A metrizability and a paracompactness of probability measures spaces, Vestn. Mosk. Univ. Ser. Matem., Mekh. N1 (1993), 14-17.
A. V. Arhangel'skii, An addition theorem for the weight of sets lying in bicompacta, Dokl. Akad. Nauk. SSSR. 126 (1959), N2, 239-241.
A. V. Arhangel'skii, On a class of spaces containing all metric spaces and all locally bicompact spaces, Matem. Sbornik. 67 (1965), N1, 55-85.
V. N. Basmanov, Covariant functors, retracts, and dimension, Dokl. Akad. Nauk SSSR. 271 (1983), N5, 1033-1036.
C. J. R. Borges, On stratifiable spaces, Pacif. J. Math. 17 (1966), N1, 1-16.
J. G. Ceder, Some generalizations of metric spaces, Pacif. J. Math. 11 (1961), 105-125. http://dx.doi.org/10.2140/pjm.1961.11.105
A. Ch. Chigogidze, Extension of normal functors, Vestn. Mosc. Univ. Ser. Matem., Mekh. N6 (1984), 40-42.
R. Engelking, General Topology, Warszawa, PWN. 1977.
V. V. Fedorchuk and V. V. Filippov, General Topology: Basic Constructions, Moscow, Mosc. State Univ. 1988.
V. V. Filippov, On a perfect image of a paracompact p-space, Dokl. Akad. Nauk SSSR. 176 (1967), N3, 533-536.
G. Gruenhage, Generalized metric spaces, in Handbook of Set-Theoretic Topology. Amsterdam. 1984. Ch. 10, 423-501.
R. W. Heath and R. E. Hodel, Characterization of -spaces, Fund. Math. 77 (1973), N3, 271-275.
E. Michael, Another note on paracompact spaces, Proc. Amer. Math. Soc. 8 (1957), 822-828. http://dx.doi.org/10.1090/S0002-9939-1957-0087079-9
E. Michael, Yet another note on paracompact spaces, Proc. Amer. Math. Soc. 10 (1959), 309-315. http://dx.doi.org/10.1090/S0002-9939-1959-0105668-1
K. Nagami, Σ-spaces, Fund. Math. 65 (1969), 169-192.
A. Okuyama, Some generalizations of metric spaces, their metrization theorems, and product spaces, Sci. Rep. Tokyo-Kyoiku-Daigaku. Sect.-A. 9 (1968), 236-254.
E. V. Shcepin, Functors and uncountable powers of compact spaces, Uspekhi Matem. Nauk. 36 (1981), N3, 3-62.
T. F. Zhuraev, On projectively quotient functors, (submitted).
