The Tietze-Urysohn Theorem states that every continuous real-valued function defined on a closed subspace of a normal space can be extended to a continuous function on the whole space. We prove an effective version of this theorem in the Type Two Model of Effectivity (TTE). Moreover, we introduce for qcb-spaces a slightly weaker notion of normality than the classical one and show that this prop...

For Denjoy–Carleman differential function classes C where the weight sequence M = (Mk) is logarithmically convex, stable under derivations, and non-quasianalytic of moderate growth, we prove the following: A mapping is C if it maps C -curves to C -curves. The category of C -mappings is cartesian closed in the sense that C (E, C (F, G)) = C (E × F, G) for convenient vector spaces. Applications t...

Some properties of minimal open sets and maximal open sets are studied in [1, 2]. In this paper, we define dual concepts of them, namely, maximal closed set and minimal closed set. These four types of subsets appear in finite spaces, for example. More generally, minimal open sets and maximal closed sets appear in locally finite spaces such as the digital line. Minimal closed sets and maximal op...

Here we try to distinguish and compare different notions of real closedness mainly one developed by N. Schwartz in his Habilitationschrift and the other developed by A. Sankaran and K. Varadarajan in [SV] which we shall call real closed *. We stick to the definition of real closed rings as defined and characterized in [RCR] and we try to determine and characterize real closed rings that are rea...

The purpose of the present paper is to introduce the concept of generalized closed sets in Čech closure spaces and investigate some of their characterizations. 2000 Mathematics Subject Classification: 54A05.

It is well-known that if T is an everywhere defined bounded operator on a Banach space X to a Banach space Y and T* is its adjoint, then the range R(T*) of T* is closed in X* if and only if the range R(T) of T is closed in Y (cf. [2, pp. 487-489]). The object of this note is to establish this result for closed but possibly unbounded operators. This result, for the unbounded case, is of great ut...

A category $mathbf{C}$ is called Cartesian closed  provided that it has finite products and for each$mathbf{C}$-object $A$ the functor $(Atimes -): Ara A$ has a right adjoint. It is well known that the category $mathbf{TopFuzz}$  of all topological fuzzes is both complete  and cocomplete, but it is not Cartesian closed. In this paper, we introduce some Cartesian closed subcategories of this cat...

there are only a few, non-evidence based, neuroprotective strategies for treatment and prevention of brain injuries after closed head trauma. to establish new therapy strategies, a novel animal model is needed. the aim of our investigation was to link standardized small animal models and actual patient medical care. data of experimental small animal studies often cannot be transferred to cns in...

Low, minimal flow and closed circuit anesthesia has been pursued since the beginning of the history of anesthesia. For many decades this form of anesthesia has been restricted to devoted enthusiasts and those very fond of gas kinetics. For most clinicians, selecting a fresh flow gas higher than 3-5 L/min was widely accepted as a routine anesthesia technique. The introduction onto the market of ...

The use of contextual information can significantly aid scene understanding of surveillance video. Just detecting people and tracking them does not provide sufficient information to detect situations that require operator attention.We propose a proof-of-concept system that uses several sources of contextual information to improve scene understanding in surveillance video. The focus is on two sc...