Essential extensions of Hausdorff spaces

Abstract Galego and Samuel showed that if K, L are metrizable, compact, Hausdorff spaces, then $C(K)\widehat{\otimes}_\pi C(L)$ is c0-saturated if and only if it is subprojective if and only if K and L are both scattered. We remove the hypothesis of metrizability from their result and extend it from the case of the twofold projective tensor product to the general n-fold projective tensor product to show that for any $n\in\mathbb{N}$ and compact, Hausdorff spaces K1, …, K n , $\widehat{\otimes}_{\pi, i=1}^n C(K_i)$ is c0-saturated if and only if it is subprojective if and only if each K i is scattered.

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On modal logics arising from scattered locally compact Hausdorff spaces

Annals of Pure and Applied Logic ◽

10.1016/j.apal.2018.12.005 ◽

2019 ◽

Vol 170 (5) ◽

pp. 558-577

Author(s):

Guram Bezhanishvili ◽

Nick Bezhanishvili ◽

Joel Lucero-Bryan ◽

Jan van Mill

Keyword(s):

Modal Logics ◽

Hausdorff Spaces ◽

Locally Compact

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Two semigroups of continuous relations

Journal of the Australian Mathematical Society ◽

10.1017/s144678870001733x ◽

1977 ◽

Vol 23 (1) ◽

pp. 46-58 ◽

Cited By ~ 2

Author(s):

A. R. Bednarek ◽

Eugene M. Norris

Keyword(s):

Large Class ◽

Algebraic Structure ◽

Topological Spaces ◽

Hausdorff Spaces ◽

Completely Regular ◽

Topological Semigroups ◽

Stone Type

SynopsisIn this paper we define two semigroups of continuous relations on topological spaces and determine a large class of spaces for which Banach-Stone type theorems hold, i.e. spaces for which isomorphism of the semigroups implies homeomorphism of the spaces. This class includes all 0-dimensional Hausdorff spaces and all those completely regular Hausdorff spaces which contain an arc; indeed all of K. D. Magill's S*-spaces are included. Some of the algebraic structure of the semigroup of all continuous relations is elucidated and a method for producing examples of topological semigroups of relations is discussed.

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On essential extensions of rings

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700013368 ◽

1987 ◽

Vol 35 (3) ◽

pp. 379-386 ◽

Cited By ~ 6

Author(s):

E. R. Puczyłwski

Keyword(s):

Ring Theory ◽

Essential Ideal ◽

Essential Extensions

This paper concerns the problem of description of the set of rings containing a given ring as an essential ideal. The results obtained are applied to some problems of ring theory and radicals.

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