Wallman compactification and zero-dimensionality.
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Arenas, F.G., Sánchez-Granero, M.A. (1999)
Divulgaciones Matemáticas
M. Henriksen, J. Vermeer, R. G. Woods (1989)
Alessandro Caterino, Maria Cristina Vipera (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Let be a vector sublattice over which separates points from closed sets of . The compactification obtained by embedding in a real cube via the diagonal map, is different, in general, from the Wallman compactification . In this paper, it is shown that there exists a lattice containing such that . In particular this implies that . Conditions in order to be are given. Finally we prove that, if is a compactification of such that is -dimensional, then there is an algebra such...
Z. Petrićević (1990)
Matematički Vesnik
Takashi Kimura, Chieko Komoda (2008)
Commentationes Mathematicae Universitatis Carolinae
In this paper we give a characterization of a separable metrizable space having a metrizable S-weakly infinite-dimensional compactification in terms of a special metric. Moreover, we give two characterizations of a separable metrizable space having a metrizable countable-dimensional compactification.
A. Caterino, M. C. Vipera (1988)
Rendiconti del Seminario Matematico della Università di Padova
Themba Dube (2017)
Mathematica Bohemica
Let be a completely regular Hausdorff space and, as usual, let denote the ring of real-valued continuous functions on . The lattice of -ideals of has been shown by Martínez and Zenk (2005) to be a frame. We show that the spectrum of this lattice is (homeomorphic to) precisely when is a -space. This we actually show to be true not only in spaces, but in locales as well. Recall that an ideal of a commutative ring is called a -ideal if whenever two elements have the same annihilator and...
Martin Maria Kovár (1995)
Commentationes Mathematicae Universitatis Carolinae
The problem, whether every topological space has a weak compact reflection, was answered by M. Hušek in the negative. Assuming normality, M. Hušek fully characterized the spaces having a weak reflection in compact spaces as the spaces with the finite Wallman remainder. In this paper we prove that the assumption of normality may be omitted. On the other hand, we show that some covering properties kill the weak reflectivity of a noncompact topological space in compact spaces.
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