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Compactness in constructive analysis revisited

Christoph Kreitz, Klaus Weihrauch
1987 Annals of Pure and Applied Logic  
Since p--c 6, by [ Compactness in constructive analysis revisited 35 Now assume r(q) ~_ dom(/5(p)) and ~(p)(r(q)) ~_ [.3 Cr. Then r(q) ~_ [_J C~<p,,>.  ...  Theorems concerning functions continuous on compact sets are investigated relative to constructivity properties and it is shown that usually topological properties (i.e., discontinuity) are the true reasons  ... 
doi:10.1016/0168-0072(87)90010-8 fatcat:k7zmbe6fdbe7tbj6puqfguhbmu

Page 368 of Mathematical Reviews Vol. , Issue 99a [page]

1991 Mathematical Reviews  
We also obtain that for a locally compact space X the tightness of (2*,t¢) and the character of (2*, 7) coincide. We construct a space Y such that 1((2”,t¢)) 4 max{d.(Y),kL,(Y),x7(Y)}.  ...  Jorge Galindo and Salvador Hernandez, On a theorem of van Douwen (109-113 (electronic)); Sina Greenwood and David Gauld, Microbundles revisited (114-119 (electronic)); B.  ... 

Page 541 of Mathematical Reviews Vol. 57, Issue 2 [page]

1979 Mathematical Reviews  
., closed, continuous, and having countably compact fibers) map onto a metric space.  ...  revisited. General Topology and Appl. 8 (1978), no. 1, 63-66. We assume that all spaces are completely regular and Hausdorff.  ... 

The spherical Tokamak path to fusion power — Revisited

A Sykes, M. P. Gryaznevich, D. Kingham, A. E. Costley, J. Hugill, G. Smith, P. Buxton, K. Gibson, H. R. Wilson, S. Ball, S. Chappell, Z. Melhem
2013 2013 IEEE 25th Symposium on Fusion Engineering (SOFE)  
With new advances in ST physics and relevant technologies, we revisit these proposals on the ST path to fusion power.  ...  Compact spherical tokamaks (ST) have been proposed by Stambaugh et al, [1], as a pilot plant for an ST power reactor; and by Hender et al, [2], as a powerful neutron source in this case with Q fus (P fus  ...  Several steps can be considered on this revisited ST path to fusion power.  ... 
doi:10.1109/sofe.2013.6635358 fatcat:kqlkgexszffgdlglfqet4xf2de

Page 1899 of Mathematical Reviews Vol. , Issue 2004c [page]

2004 Mathematical Reviews  
Finally the authors revisit some examples of J. Dixmier [Ann. of Math. (2) 59 (1954), 279-286; MR 15, 539b] and show that the singular MASAs constructed by Dixmier are actually strongly singular.  ...  Summary: “Let G be a locally compact group, and let T be a representation of G in a Banach space.  ... 

Page 376 of Mathematical Reviews Vol. , Issue 90A [page]

1990 Mathematical Reviews  
Fundamental constructions (also preservation of proper- ties by constructions, reflections and coreflections); 4. Separation properties (7;, 72, regular and uniform spaces); 5.  ...  Uniformly continuous mappings (also proximally continuous mappings, projective and inductive genera- tions); 3.  ... 

Page 5366 of Mathematical Reviews Vol. , Issue 95i [page]

1995 Mathematical Reviews  
95i:46108 Examples of algebras of continuous functions on (pathological) locally compact spaces show that these bounds are attained.  ...  revisited with an application to linear communication channels.  ... 

Page 6234 of Mathematical Reviews Vol. , Issue 2000i [page]

2000 Mathematical Reviews  
and f (t,x) is globally Lipschitz continuous in x in the space (#',d,,) uniformly in ¢ € [0, 7].  ...  , d,.) of normal, fuzzy convex, upper semi-continuous fuzzy sets with compact support in R', i.e. fuzzy numbers, where the metric d,, is the supremum over the membership grade of the Hausdorff metric distances  ... 

Classical Morse theory revisited - I backward $\lambda$-lemma and homotopy type

Joa Weber
2016 Topological Methods in Nonlinear Analysis  
Dynamical thickening leads to a conceptually simple and short proof.  ...  We introduce two tools, dynamical thickening and flow selectors, to overcome the infamous discontinuity of the gradient flow endpoint map near non-degenerate critical points.  ...  The function T A is lower and upper semi-continuous, hence continuous, because the subset A of Z is closed and forward flow invariant, respectively; cf. [4, Pf. of Thm. B].  ... 
doi:10.12775/tmna.2016.020 fatcat:vflpehqc7rgwxn5t35w3xdvu74

David B. Ellis and Robert Ellis Automorphisms and equivalence relations in topological dynamics (Cambridge University Press, 2014), 281 pp, 978-1-107-63322-3 (paperback), £45/$70

Tom Ward
2015 Proceedings of the Edinburgh Mathematical Society  
The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes  ...  The second author introduced [2] the enveloping semigroup of a topological dynamical system (X, G), where X is a compact Hausdorff space and G is a topological group acting continuously on X by homeomorphisms  ...  algebraic origin) remain of great interest, the abstract theory of continuous maps on compact topological spaces has its own interesting history.  ... 
doi:10.1017/s0013091515000607 fatcat:ffotj2qmpzgp7mvybq3ej3pee4

The normality of products with one compact factor, revisited

Amer Bešlagić
1993 Topology and its Applications  
., The normality of products with one compact factor, revisited, Topology and its Applications 52 (1993) 121-126.  ...  A simpler proof of the following theorem by Rudin is given: If C is compact, X x C normal, and Y a closed image of X, then Y X C is normal.  ...  Introduction All spaces are Hausdorff and all maps are continuous. For all undefined notation and terminology, and the facts that are used without mention, we refer the reader to [4] .  ... 
doi:10.1016/0166-8641(93)90031-8 fatcat:unsf25vierce3mmzbavjsyhxae

Robust Asymptotic Stabilization of Hybrid Systems using Control Lyapunov Functions

Ricardo G. Sanfelice
2016 Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control - HSCC '16  
We propose tools for the study of robust stabilizability and the design of robustly stabilizing feedback laws for a wide class of hybrid systems given in terms of hybrid inclusions with inputs and disturbances  ...  (x, u⋆, w⋆) ∈ K } • The projector onto the state and input space ∆⋆(r, K) := (x, u⋆) : ∃w⋆ s.t. (x, u⋆, w⋆) ∈ K ∩ (I(r) × R m⋆ × R d⋆ ) • The projector onto the input and disturbance space  ...  (controlled pendulum with impacts (revisited)) A robust control Lyapunov function satisfying the conditions in Theorem 4.1 was constructed in Example 3.7.  ... 
doi:10.1145/2883817.2883848 dblp:conf/hybrid/Sanfelice16 fatcat:sj65wm4lzbc4lpau7sytvqfy4a

Page 9365 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
Finally, the Aleksandrov double is used to construct a space that is countably compact locally compact and scattered, but is not «-normal.  ...  In normal topological spaces X, for every two functions g,h: X — IR satisfying g < A with g upper semicontinuous and / lower semi- continuous, there exists a continuous function f: X — R satisfying g <  ... 

Page 5523 of Mathematical Reviews Vol. , Issue 99h [page]

1999 Mathematical Reviews  
Finally, special pairs each member of which is the union of mutually disjoint (nontrivial) compact intervals in the real line are constructed. Several open questions are also posed.  ...  We investigate some properties such as, e.g., compactness and completeness of these approach structures.  ... 

Page 1245 of Mathematical Reviews Vol. , Issue 2004b [page]

2004 Mathematical Reviews  
Summary: “We revisit D. J. White’s theorem in [J. London Math.  ...  Finally we de- fine two new kinds of generalized continuous functions by means of connected and compact sets and study their relations with other weak forms of continuity and their behaviours under operations  ... 
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