A note on the metrization of -spaces

Author:
Harold W. Martin

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

MSC:
Primary 54E35

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

MathSciNet review:
0413056

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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*, Uspehi Mat. Nauk**21**(1966), no.**4**(130), 133-184 = Russian Math. Surveys**21**(1966), no.**4**, 115-162. MR**37**#3534. MR**0227950 (37:3534)****[2]**J. G. Ceder,*Some generalizations of metric spaces*, Pacific J. Math.**11**(1961), 105-125. MR**24**#A1707. MR**0131860 (24:A1707)****[3]**P. Fletcher and W. F. Lindgren,*Locally quasi-uniform spaces with countable bases*, Duke Math. J.**41**(1974), 231-240. MR**49**#6173. MR**0341422 (49:6173)****[4]**R. W. Heath,*On open mappings and certain spaces satisfying the first countability axiom*, Fund. Math.**57**(1965), 91-96. MR**131**#4006. MR**0179763 (31:4006)****[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**45**#2657. MR**0293580 (45:2657)****[6]**-,*Some results in metrization theory*, 1950-1972, Topology Conference (Virginia Polytech. Inst. and State Univ., Blacksburg, Va., 1973), Lecture Notes in Math., vol. 375, Springer-Verlag, Berlin, 1974, pp. 120-136. MR**50**#8459. MR**0355986 (50:8459)****[7]**-,*Metrizability of topological spaces*(to appear).**[8]**T. Hoshina,*On the quotient -images of metric spaces*, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A**10**(1970), 265-268. MR**43**# 1115. MR**0275358 (43:1115)****[9]**D. J. Lutzer,*Semimetrizable and stratifiable spaces*, General Topology and Appl.**1**(1971), no. 1, 43-48. MR**45**#5952. MR**0296893 (45:5952)****[10]**H. W. Martin,*Metrization of symmetric spaces and regular maps*, Proc. Amer. Math. Soc.**35**(1972), 269-274. MR**46**#2648. MR**0303511 (46:2648)****[11]**-,*Metrization and submetrization of topological spaces*, Dissertation, University of Pittsburgh, 1973.**[12]**-,*Weak bases and metrization*, Trans. Amer. Math. Soc. (to appear). MR**0423311 (54:11290)****[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]**R. R. Sabella,*Convergence properties of neighboring sequences*, Proc. Amer. Math. Soc.**38**(1973), 403-409. MR**47**#1036. MR**0312479 (47:1036)****[15]**T. Shiraki,*On some metrization theorems*(to appear).**[16]**F. Siwiec,*Generalizations of the first axiom of countability*, Rocky Mountain J. Math.**5**(1975), 1-60. MR**0358699 (50:11158)**

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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