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Ultra L I -ideals in lattice implication algebras

Ke Yun Qin, Yang Xu, Young Bae Jun (2002)

Czechoslovak Mathematical Journal

We define an ultra L I -ideal of a lattice implication algebra and give equivalent conditions for an L I -ideal to be ultra. We show that every subset of a lattice implication algebra which has the finite additive property can be extended to an ultra L I -ideal.

Ultra L I -Ideals in lattice implication algebras and M T L -algebras

Xiaohong Zhang, Ke Yun Qin, Wiesław Aleksander Dudek (2007)

Czechoslovak Mathematical Journal

A mistake concerning the ultra L I -ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an L I -ideal to be an ultra L I -ideal are given. Moreover, the notion of an L I -ideal is extended to M T L -algebras, the notions of a (prime, ultra, obstinate, Boolean) L I -ideal and an I L I -ideal of an M T L -algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in M T L -algebra: (1) prime proper L I -ideal and Boolean L I -ideal,...

Ultrametric spaces bi-Lipschitz embeddable in n

Kerkko Luosto (1996)

Fundamenta Mathematicae

It is proved that if an ultrametric space can be bi-Lipschitz embedded in n , then its Assouad dimension is less than n. Together with a result of Luukkainen and Movahedi-Lankarani, where the converse was shown, this gives a characterization in terms of Assouad dimension of the ultrametric spaces which are bi-Lipschitz embeddable in n .

Uniform maps into normed spaces

Zdeněk Frolìk (1974)

Annales de l'institut Fourier

Thirteen properties of uniform spaces are shown to be equivalent. The most important properties seem to be those related to modules of uniformly continuous mappings into normed spaces, and to partitions of unity.

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