Closed mappings of nowhere locally compact metric spaces

Stricklen, S. A.

doi:10.1090/S0002-9939-1978-0478114-8

Closed mappings of nowhere locally compact metric spaces
HTML articles powered by AMS MathViewer

by S. A. Stricklen

Proc. Amer. Math. Soc. 68 (1978), 369-374

DOI: https://doi.org/10.1090/S0002-9939-1978-0478114-8

PDF | Request permission

Abstract:

We present a method of construction which allows us to construct many examples of nowhere first countable spaces which are images of metric spaces under closed mappings, and which allows us to prove (with a certain natural restriction on the mapping) that there is a closed mapping from a metric space M onto a space with a dense nowhere first countable subspace if and only if M is nowhere locally compact.

References

R. L. Moore, Foundations of point set theory, Revised edition, American Mathematical Society Colloquium Publications, Vol. XIII, American Mathematical Society, Providence, R.I., 1962. MR 0150722
N. Lašnev, On continuous decompositions and closed mappings of metric spaces, Dokl. Akad. Nauk SSSR 165 (1965), 756–758 (Russian). MR 0192478
Kiiti Morita, On closed mappings, Proc. Japan Acad. 32 (1956), 539–543. MR 85494
Kiiti Morita and Sitiro Hanai, Closed mappings and metric spaces, Proc. Japan Acad. 32 (1956), 10–14. MR 87077
A. H. Stone, Metrizability of decomposition spaces, Proc. Amer. Math. Soc. 7 (1956), 690–700. MR 87078, DOI 10.1090/S0002-9939-1956-0087078-6

Concerning closed, continuous images of metric spaces

K. R. Van Doren, Closed, continuous images of complete metric spaces, Fund. Math. 80 (1973), no. 1, 47–50. MR 358674, DOI 10.4064/fm-80-1-47-50