Let $L$ be a completely regular frame and $mathcal{R}L$ be the ‎ring of continuous real-valued functions on $L$‎. ‎We show that the‎ ‎lattice $Zid(mathcal{R}L)$ of $z$-ideals of $mathcal{R}L$ is a‎ ‎normal coherent Yosida frame‎, ‎which extends the corresponding $C(X)$‎ ‎result of Mart'{i}nez and Zenk‎. ‎This we do by exhibiting‎ ‎$Zid(mathcal{R}L)$ as a quotient of $Rad(mathcal{R}L)$‎, ‎the‎ ‎...

We study countable saturation of metric reduced products and introduce continuous fields of metric structures indexed by locally compact, separable, completely metrizable spaces. Saturation of the reduced product depends both on the underlying index space and the model. By using the Gelfand–Naimark duality we conclude that the assertion “Stone–Čech remainder of the half-line has only trivial au...

Let me begin by expressing my sincere gratitude to the Japanese Association of Mathematical Sciences for inviting me to present this lecture and for giving me the JAMS International Prize for 2003 . I am deeply honored. This lecture is not a survey, but simply a discussion of some topics that I find interesting. For the most recent surveys of this subject area in which I have participated see [...

Recently [4] we have obtained some new algebraic results about βN, the Stone-Čech compactification of the discrete set of positive integers and about βW , where W is the free semigroup over a nonempty alphabet with infinitely many variables adjoined. (The results about βW extend the Graham-Rothschild Parameter Sets Theorem.) In this paper we derive some Ramsey Theoretic consequences of these re...

I n October 2001, a National Academies committee was convened to examine the responsibilities of authorship in the biological sciences. This blue ribbon group was drawn broadly from academia, the commercial sector, and scientific publishing and was chaired by Tom Cech, president of the Howard Hughes Medical Institute. The committee evaluated the responsibilities of authors to share data and mat...

The generalised structural arrangements of various bimolecule such as carbohydrates, proteins etc are based on the rules ofČech closure operator. In this paper we discuss the relationship betweeň Cech closure space and structural configuration of proteins.

We show that Haefliger's cohomology forétale groupoids, Moore's cohomology for locally compact groups and the Brauer group of a locally compact groupoid are all particular cases of sheaf (oř Cech) cohomology for topological simplicial spaces.

Thomas Cech shared the 1989 Nobel Prize for Chemistry with Sidney Altman (Enzymatic cleavage of RNA by RNA. Biosci. Rep. 10:317–337, 1990). That year we also published the lectures by the winners of the Physiology or Medicine prize: Harold E Varmus (Retroviruses and oncogenes I. Biosci. Rep. 10:413–430, 1990) and J Michael Bishop (Retroviruses and oncogenes II. Biosci. Rep. 10:473–491, 1990) an...

The lattice of ordered compactifications of a topological sum of a finite number of totally ordered spaces is investigated. This investigation proceeds by decomposing the lattice into equivalence classes determined by the identification of essential pairs of singularities. This lattice of equivalence classes is isomorphic to a power set lattice. Each of these equivalence classes is further deco...