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Compactness in constructive analysis revisited

1987
*
Annals of Pure and Applied Logic
*

Since p--c 6, by [

doi:10.1016/0168-0072(87)90010-8
fatcat:k7zmbe6fdbe7tbj6puqfguhbmu
*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 ...##
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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

2013
*
2013 IEEE 25th Symposium on Fusion Engineering (SOFE)
*

With new advances in ST physics

doi:10.1109/sofe.2013.6635358
fatcat:kqlkgexszffgdlglfqet4xf2de
*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. ...##
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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. ...##
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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. ...##
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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 ...

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

2016
*
Topological Methods in Nonlinear Analysis
*

Dynamical thickening leads to a conceptually simple

doi:10.12775/tmna.2016.020
fatcat:vflpehqc7rgwxn5t35w3xdvu74
*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]. ...##
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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

2015
*
Proceedings of the Edinburgh Mathematical Society
*

The full-text may be used

doi:10.1017/s0013091515000607
fatcat:ffotj2qmpzgp7mvybq3ej3pee4
*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. ...##
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The normality of products with one compact factor, revisited

1993
*
Topology and its Applications
*

., The normality of products with one

doi:10.1016/0166-8641(93)90031-8
fatcat:unsf25vierce3mmzbavjsyhxae
*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] . ...##
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Robust Asymptotic Stabilization of Hybrid Systems using Control Lyapunov Functions

2016
*
Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control - HSCC '16
*

We propose tools for the study of robust stabilizability

doi:10.1145/2883817.2883848
dblp:conf/hybrid/Sanfelice16
fatcat:sj65wm4lzbc4lpau7sytvqfy4a
*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. ...##
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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 < ...##
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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. ...##
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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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