Research and Innovation Articles
Published 2020-01-24
Keywords
- Moore’s space,
- independence,
- continuum hypothesis,
- Martin’s Axiom,
- Q-set
How to Cite
Parra-Londoño, C. M., & Uribe-Zapata, A. F. (2020). The independence of a weak version of the normal Moore space conjecture. Revista Integración, Temas De matemáticas, 38(1), 43–54. https://doi.org/10.18273/revint.v38n1-2020004
Abstract
Our purpose is to present an elementary exposition of a classical
result in general topology which is a weak version of a problem known as the
normal Moore space conjecture. With this aim we study some of the basic
properties of Moore spaces and characterize those which are both Lindelof
and second countable. We also make use of the continuum hypothesis along
with Martin’s axiom to establish the result in question.
Downloads
Download data is not yet available.
References
[1] Bing R.H., “Metrization of topological spaces”, Canad. J. Math. 3 (1951), 175–186.
[2] Fleissner W.G., “Normal nonmetrizable Moore space from continuum hypothesis
or nonexistence of inner models with measurable cardinals”, Proc. Nat. Acad. Sci.
U.S.A. 79 (1982), No. 4, 1371–1372.
[3] Jones F.B., “Concerning normal and completely normal space”, Bull. Am. Math.
Soc. 47 (1937), 671–677.
[4] Kunen K., Set Theory: An introduction to independence proofs, North-Holland Publishing
Co., Amsterdam, 1980.
[5] Nyikos P.J., “A provisional solution to the normal Moore space problem”, Proc.
Amer. Math. Soc. 78 (1980), No. 3, 429–435.
[6] Tall F.D., “Set-theoretic consistency results and topological theorems concerning the
normal Moore space conjecture and related problems”, Thesis (Ph. D), University
of Wisconsin, Madison, 1969, 53 p.
[7] Uribe-Zapata Andrés F., “Sobre la independencia de la hipótesis del espacio normal
de Moore”, Trabajo de grado en Matemáticas, Universidad Nacional de Colombia,
Medellín, 2019, 70 p.
[2] Fleissner W.G., “Normal nonmetrizable Moore space from continuum hypothesis
or nonexistence of inner models with measurable cardinals”, Proc. Nat. Acad. Sci.
U.S.A. 79 (1982), No. 4, 1371–1372.
[3] Jones F.B., “Concerning normal and completely normal space”, Bull. Am. Math.
Soc. 47 (1937), 671–677.
[4] Kunen K., Set Theory: An introduction to independence proofs, North-Holland Publishing
Co., Amsterdam, 1980.
[5] Nyikos P.J., “A provisional solution to the normal Moore space problem”, Proc.
Amer. Math. Soc. 78 (1980), No. 3, 429–435.
[6] Tall F.D., “Set-theoretic consistency results and topological theorems concerning the
normal Moore space conjecture and related problems”, Thesis (Ph. D), University
of Wisconsin, Madison, 1969, 53 p.
[7] Uribe-Zapata Andrés F., “Sobre la independencia de la hipótesis del espacio normal
de Moore”, Trabajo de grado en Matemáticas, Universidad Nacional de Colombia,
Medellín, 2019, 70 p.