Paracompactness in perfectly normal, locally connected, locally compact spaces

Paracompactness in perfectly normal, locally connected, locally compact spaces
HTML articles powered by AMS MathViewer

by Diane J. Lane PDF

Proc. Amer. Math. Soc. 80 (1980), 693-696 Request permission

It is shown that, under $({\text {MA}} + \neg {\text {CH}})$, every perfectly normal, locally compact and locally connected space is paracompact.

References

K. Alster and P. L. Zenor, On the collectionwise normality of generalized manifolds, Topology Proceedings, Vol. I (Conf., Auburn Univ., Auburn, Ala., 1976) Math. Dept., Auburn Univ., Auburn, Ala., 1977, pp. 125–127. MR 0451199
J. Chaber and P. Zenor, On perfect subparacompactness and a metrization theorem for Moore spaces, Topology Proc. 2 (1977), no. 2, 401–407 (1978). MR 540618
I. Juhász, Cardinal functions in topology, Mathematical Centre Tracts, No. 34, Mathematisch Centrum, Amsterdam, 1971. In collaboration with A. Verbeek and N. S. Kroonenberg. MR 0340021
G. M. Reed and P. L. Zenor, Metrization of Moore spaces and generalized manifolds, Fund. Math. 91 (1976), no. 3, 203–210. MR 425918, DOI 10.4064/fm-91-3-203-210
Mary Ellen Rudin, The undecidability of the existence of a perfectly normal nonmetrizable manifold, Houston J. Math. 5 (1979), no. 2, 249–252. MR 546759
Mary Ellen Rudin and Phillip Zenor, A perfectly normal nonmetrizable manifold, Houston J. Math. 2 (1976), no. 1, 129–134. MR 394560

S-spaces and L-spaces under Martin’s Axiom