The Fundamental Group as the Structure of a Dually Affine Space

This paper dualizes the setting of affine spaces as originally introduced by Diers for application to algebraic geometry and expanded upon by various authors, to show that the fundamental groups of pointed topological spaces appear as the structures of dually affine spaces. The dual of the Zariski closure operator is introduced, and the 1-sphere and its copowers together with their fundamental groups are shown to be examples of complete objects with respect to the Zariski dual closure operator.     

Bases of topological epi-reflections

In the first part of this paper a characterization of epi-reflective subcategories of the category TOP of topological spaces in terms of initial topologies is given. This characterization enables us to associate to each epi-reflective subcategory of TOP, regular systems of cogenerators. After having examined some properties of these regular systems, the second part of the paper considers an A-closure operator associated to every epi-reflective subcategory A of TOP which for each regular system of cogenerators of A determines an epi-reflective subcategory of A.     

Onm-separated projection spaces

Closure operators in the category of projection spaces are investigated. It is shown that completeness, absolutes-closure ands-injectivity coincide in the subcategory of separated projection spaces and that there compactness with respect to projections implies completeness.Dedicated to Nico Pumplün on the occasion of his 60th birthdayPartial financial support by the Italian Ministry of Public Education is gratefully acknowledged.     

A Topologist’s View of Chu Spaces

For a symmetric monoidal-closed category $\mathcal{X}$ and any object K, the category of K-Chu spaces is small-topological over $\mathcal{X}$ and small cotopological over $\mathcal{X}^{{{\text{op}}}}$ . Its full subcategory of $\mathcal{M}$ -extensive K-Chu spaces is topological over $\mathcal{X}$ when $\mathcal{X}$ is $\mathcal{M}$ -complete, for any morphism class $\mathcal{M}$ . Often this subcategory may be presented as a full coreflective subcategory of Diers’ category of affine K-spaces. Hence, in addition to their roots in the theory of pairs of topological vector spaces (Barr) and their connections with linear logic (Seely), the Dialectica categories (Hyland, de Paiva), and with the study of event structures for modeling concurrent processes (Pratt), Chu spaces seem to have a less explored link with algebraic geometry. We use the Zariski closure operator to describe the objects of the *-autonomous category of $\mathcal{M}$ -extensive and $\mathcal{M}$ -coextensive K-Chu spaces in terms of Zariski separation and to identify its important subcategory of complete objects.     

Automated image-based method for laboratory screening of coating libraries for adhesion of algae and bacterial biofilms

Assessment and down-selection of non-biocidal coatings that prevent the adhesion of fouling organisms in the marine environment requires a hierarchy of laboratory methods to reduce the number of experimental coatings for field testing. Automated image-based methods are described that facilitate rapid, quantitative biological screening of coatings generated through combinatorial polymer chemistry. Algorithms are described that measure the coverage of bacterial and algal biofilms on coatings prepared in 24-well plates and on array panels, respectively. The data are used to calculate adhesion strength of organisms on experimental coatings. The results complement a number of physical and mechanical methods developed to screen large numbers of samples.     

Capillary electrophoresis with laser-induced fluorescence detection for ATP quantification in spermatozoa and oocytes

We describe a new capillary electrophoresis laser-induced fluorescence (CE-LIF) method for the quantification of adenosine 5′-triphosphate (ATP) in spermatozoa and oocytes. The optimization of the precapillary derivatization reaction between ATP and 4,4-difluoro-5,7-dimethyl-4-bora-3a,4adiaza-s-indacene-3-propionyl ethylene diamine hydrochloride (BODIPY FL EDA) has been described. BODIPY-ATP conjugate was analysed in an uncoated fused silica capillary of 75 μm ID and 50 cm effective length using a 10 mmol/L tribasic sodium phosphate buffer, pH 11.5, at 22 kV in <5 min. A good reproducibility of intra- and inter-assay tests was obtained (CV?=?4.55% and 7.14%, respectively). With respect to our previous CE-UV assay, the new method showed an improvement in sensitivity that was about 120-fold (limit of quantification, 0.15 vs 18 μmol/L). Method applicability was proven on the reproductive cells of several animal species (roosters, horses, sheep and goats). Due to the elevated sensitivity, the new assay allows the measurement of adenosine 5′-triphosphate levels from just 20 oocytes. Considering that ATP concentration in reproductive cells is related to the mitochondrial integrity after cryopreservation, the proposed method could be a useful tool in assisted reproductive technologies.     

Factorizations,injectivity and compactness in categories of modules

A notion of closure operator for modules is used to characterize factorization structures in categories of modules. Moreover compactness, injectivity and absolute closedness are studied with respect to such closure operators. A criterion for compactness of modules is obtained in terms of injectivity or absolute closedness of the quotients extending recent results of Temple Fay.     

What is a Quotient Map with Respect to a Closure Operator?

It is shown that there is no good answer to the question of the title, even if we restrict our attention to S et-based topological categories. Although very closely related, neither the natural notion of c-finality (designed in total analogy to c-initiality) nor the notion of c-quotient (modelled after the behaviour of topological quotient maps) provide universally satisfactory concepts. More dramatically, in the category T op with its natural Kuratowski closure operator k, the class of k-final maps cannot be described as the class of c-quotient maps for any closure operator c, and the class of k-quotients cannot be described as the class of c-final maps for any c. We also discuss the behaviour of c-final maps under crossing with an identity map, as in Whitehead's Theorem. In T op, this gives a new stability theorem for hereditary quotient maps.