A note on the metrization of -spaces

Author:
Harold W. Martin

Journal:
Proc. Amer. Math. Soc. **57** (1976), 332-336

MSC:
Primary 54E35

MathSciNet review:
0413056

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The class of quasi Nagata spaces, which strictly includes the class of wN-spaces, is defined. A closely related class of spaces, pseudo Nagata spaces, are also defined. It is shown that a Hausdorff -space is metrizable if and only if it is either a quasi Nagata space or a pseudo Nagata space.

**[1]**A. V. Arhangel′skiĭ,*Mappings and spaces*, Russian Math. Surveys**21**(1966), no. 4, 115–162. MR**0227950****[2]**Jack G. Ceder,*Some generalizations of metric spaces*, Pacific J. Math.**11**(1961), 105–125. MR**0131860****[3]**W. F. Lindgren and P. Fletcher,*Locally quasi-uniform spaces with countable bases*, Duke Math. J.**41**(1974), 231–240. MR**0341422****[4]**R. W. Heath,*On open mappings and certain spaces satisfying the first countability axiom*, Fund. Math.**57**(1965), 91–96. MR**0179763****[5]**R. E. Hodel,*Spaces defined by sequences of open covers which guarantee that certain sequences have cluster points*, Duke Math. J.**39**(1972), 253–263. MR**0293580****[6]**R. E. Hodel,*Some results in metrization theory, 1950–1972*, Topology Conference (Virginia Polytech. Inst. and State Univ., Blacksburg, Va., 1973) Springer, Berlin, 1974, pp. 120–136. Lecture Notes in Math., Vol. 375. MR**0355986****[7]**-,*Metrizability of topological spaces*(to appear).**[8]**Takao Hoshina,*On the quotient 𝑠-images of metric spaces*, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A**10**(1970), 265–268 (1970). MR**0275358****[9]**D. J. Lutzer,*Semimetrizable and stratifiable spaces*, General Topology and Appl.**1**(1971), no. 1, 43–48. MR**0296893****[10]**Harold W. Martin,*Metrization of symmetric spaces and regular maps*, Proc. Amer. Math. Soc.**35**(1972), 269–274. MR**0303511**, 10.1090/S0002-9939-1972-0303511-5**[11]**-,*Metrization and submetrization of topological spaces*, Dissertation, University of Pittsburgh, 1973.**[12]**Harold W. Martin,*Weak bases and metrization*, Trans. Amer. Math. Soc.**222**(1976), 337–344. MR**0423311**, 10.1090/S0002-9947-1976-0423311-3**[13]**S. Nedev and M. M. Čoban,*On the theory of 0-metrizable spaces*. I, II, III, Vestnik Moskov. Univ. Ser. I Mat. Meh.**27**(1972), no. 1, 8-15; no. 2, 10-17; no. 3, 10-15. (Russian) MR**45**#4356; #4357;**46**#6312.**[14]**Ralph R. Sabella,*Convergence properties of neighboring sequences*, Proc. Amer. Math. Soc.**38**(1973), 405–409. MR**0312479**, 10.1090/S0002-9939-1973-0312479-8**[15]**T. Shiraki,*On some metrization theorems*(to appear).**[16]**Frank Siwiec,*Generalizations of the first axiom of countability*, Rocky Mountain J. Math.**5**(1975), 1–60. MR**0358699**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
54E35

Retrieve articles in all journals with MSC: 54E35

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1976-0413056-3

Keywords:
-space,
metrizable space,
Nagata space,
wN-space,
quasi Nagata space,
pseudo Nagata space

Article copyright:
© Copyright 1976
American Mathematical Society