Duality between stable strong shape morphisms and stable homotopy classes
Let SStrShn be the full subcategory of the stable strong shape category SStrSh of pointed compacta [H-N] whose objects are all pointed subcompacta of S and let SOn be the full subcategory of the stable homotopy category S ([S-W] or [S]) whose objects are all open subsets of S. In this paper it is shown that there exists a contravariant additive functor Dn : SStrShn → SOn such that Dn(X) = S \ X for every subcompactum X of S and Dn : SStrShn(X, Y ) → SOn(S \Y,S \X) is an isomorphism of abelian groups for all compacta X,Y ⊂ S. Moreover, if X ⊂ Y ⊂ S, j : S \ Y → S \ X is an inclusion and α ∈ SStrShn(X, Y ) is induced by the inclusion of X into Y then Dn(α) = {j}. Introduction. Basic definitions. In [N] it has been proved that the stable shape category of subcompacta of S is isomorphic to the stable weak homotopy category of their complements. This theorem generalizes the Spanier-Whitehead Duality Theorem and corresponds to the Chapman Complement Theorem [S1]. In [H-N] the authors have constructed a stable strong shape category of pointed metric compacta (see also [M]). The purpose of the present note is to prove that there exists a contravariant functor from the stable strong shape category of pointed subcompacta of 2000 Mathematics Subject Classification. 55P55, 55P25.
A strong-shape theoretical version of a result due to E. Lima
Abstract There exists a strong-shape theoretical version of S-duality for two compacta X , Y ⊂ S n (Theorem 1.1) which turns out to be an immediate consequence of Alexander duality for generalized (co-)homology theories Ē ∗ , Ē ∗ with coefficients in a spectrum E , as in [1]. This result transfers earlier investigations by Lima [4] from ordinary to strong shape theory.
High-Speed Infrared Radiometers*
The paper describes high-speed infrared radiometers utilizing thermistor infrared detectors. Instruments with 4- and 8-in. diam Cassegrain mirror optics are described. The method of operation and the calibration of these radiometers is discussed.The radiometers are uniformly sensitive from 0.7 to 35 μ. They have a response time of 16 msec and a sensitivity of the order of 10−10 w/cm−2 corresponding to a blackbody temperature differential of 0.01°C.The radiometers are used for quantitative measurements of infrared radiation and remote temperature determinations.