𝜎-coherent continua are hereditarily locally connected

Hagan, M. R.; Mahavier, W. S.

doi:10.1090/S0002-9939-1981-0589154-2

$\sigma$-coherent continua are hereditarily locally connected
HTML articles powered by AMS MathViewer

by M. R. Hagan and W. S. Mahavier PDF

Proc. Amer. Math. Soc. 81 (1981), 129-132 Request permission

Abstract:

A $\sigma$-coherent continuum is one in which every descending sequence of connected sets has a connected intersection. In this paper it is proved that such continua are hereditarily locally connnected. An example is given to show that the converse is not true.

References

K. M. Garg, Monotonicity of connected functions, Proc. First Conf. on Monotone Mappings and Open Mappings (SUNY at Binghamton, Binghamton, N.Y., 1970) State Univ. of New York at Binghamton, Binghamton, N.Y., 1971, pp. 351–359. MR 0279778
Melvin R. Hagan, Continuity of certain connected functions and multifunctions, Proc. Amer. Math. Soc. 42 (1974), 295–301. MR 326652, DOI 10.1090/S0002-9939-1974-0326652-7
Casimir Kuratowski, Topologie. Vol. II, Monografie Matematyczne, Tom 21, Państwowe Wydawnictwo Naukowe, Warsaw, 1961 (French). Troisième édition, corrigèe et complétée de deux appendices. MR 0133124
Harlan C. Miller, On unicoherent continua, Trans. Amer. Math. Soc. 69 (1950), 179–194. MR 36498, DOI 10.1090/S0002-9947-1950-0036498-3
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
Gordon Thomas Whyburn, Analytic topology, American Mathematical Society Colloquium Publications, Vol. XXVIII, American Mathematical Society, Providence, R.I., 1963. MR 0182943