Approximation and Extension of C∞ Functions Defined on Compact Subsets of ℂn

1989 ◽  
pp. 283-295
Author(s):  
Wiesław Pawłucki ◽  
Wiesław Pleśniak
Keyword(s):  
Compact Subsets

scholarly journals Compact Subsets of the Glimm Space of a C*-algebra

2014 ◽  
Vol 57 (1) ◽  
pp. 90-96
Author(s):  
Aldo J. Lazar
Keyword(s):  
Compact Subset ◽  
Positive Element ◽  
C Algebra ◽  
Compact Subsets

AbstractIf A is a σ-unital C*-algebra and a is a strictly positive element of A, then for every compact subset K of the complete regularization Glimm(A) of Prim(A) there exists α > 0 such that K ⊂ {G ∊ Glimm(A) | ||a + G|| ≥ α: This extends a result of J. Dauns to all σ-unital C*-algebras. However, there exist a C*-algebra A and a compact subset of Glimm(A) that is not contained in any set of the form {G ∊ Glimm(A) | ||a + G|| ≥}, a ∊ A and α > 0.

HORSESHOE IN THE HYPERCHAOTIC MCK CIRCUIT

2007 ◽  
Vol 17 (11) ◽  
pp. 4205-4211 ◽  
Author(s):  
FANGYAN YANG ◽  
QINGDU LI ◽  
PING ZHOU
Keyword(s):  
Experimental Observation ◽  
Cross Section ◽  
Physical System ◽  
Topological Horseshoe ◽  
Return Map ◽  
Poincaré Return Map ◽  
Compact Subsets

The well-known Matsumoto–Chua–Kobayashi (MCK) circuit is of significance for studying hyperchaos, since it was the first experimental observation of hyperchaos from a real physical system. In this paper, we discuss the existence of hyperchaos in this circuit by virtue of topological horseshoe theory. The two disjoint compact subsets producing a horseshoe found in a specific 3D cross-section, both expand in two directions under the fourth Poincaré return map, this fact means that there exists hyperchaos in the circuit.

scholarly journals On compact subsets of Sobolev spaces on manifolds

2020 ◽  
pp. 1
Author(s):  
Leszek Skrzypczak ◽  
Cyril Tintarev
Keyword(s):  
Sobolev Spaces ◽  
Compact Subsets

scholarly journals Functions of bounded variation on compact subsets of the plane

2005 ◽  
Vol 169 (2) ◽  
pp. 163-188 ◽  
Author(s):  
Brenden Ashton ◽  
Ian Doust
Keyword(s):  
Bounded Variation ◽  
Functions Of Bounded Variation ◽  
Compact Subsets

scholarly journals Measures and Pseudomeasures on Compact Subsets of the Line.

1968 ◽  
Vol 23 ◽  
pp. 57 ◽  
Author(s):  
Y. Katznelson ◽  
C. Mc Gehee
Keyword(s):  
Compact Subsets

Spaces with a Unique Uniformity

1983 ◽  
Vol 35 (6) ◽  
pp. 1001-1009
Author(s):  
Richard H. Warren
Keyword(s):  
Companion Paper ◽  
The Other ◽  
Completely Regular ◽  
Continuous Maps ◽  
Uniformly Continuous ◽  
Compact Subsets

The major results in this paper are nine characterizations of completely regular spaces with a unique compatible uniformity. All prior results of this type assumed that the space is Tychonoff (i.e., completely regular and Hausdorff) until the appearance of a companion paper [9] which began this study. The more important characterizations use quasi-uniqueness of R1-compactifications which relate to uniqueness of T2-comPactifications. The features of the other characterizations are: (i) compact subsets linked to Cauchy filters, (ii) C- and C*-embeddings, and (iii) lifting continuous maps to uniformly continuous maps.Section 2 contains information on T0-identification spaces which we will use later in the paper. In Section 3 several properties of uniform identification spaces are developed so that they can be used later. The nine characterizations are established in Section 4. Also it is shown that a space with a unique compatible uniformity is normal if and only if each of its closed subspaces has a unique compatible uniformity.

Holomorphic Generation of Continuous Inverse Algebras

2007 ◽  
Vol 59 (1) ◽  
pp. 3-35
Author(s):  
Harald Biller
Keyword(s):  
Banach Algebras ◽  
Holomorphic Functions ◽  
Commutative Banach Algebras ◽  
Continuous Inverse ◽  
Holomorphic Convexity ◽  
Compact Subsets

AbstractWe study complex commutative Banach algebras (and, more generally, continuous inverse algebras) in which the holomorphic functions of a fixedn-tuple of elements are dense. In particular, we characterize the compact subsets of ℂnwhich appear as joint spectra of suchn-tuples. The characterization is compared with several established notions of holomorphic convexity by means of approximation conditions.

Spaces which Cannot be Written as a Countable Disjoint Union of Closed Subsets

1973 ◽  
Vol 16 (3) ◽  
pp. 435-437 ◽  
Author(s):  
C. Eberhart ◽  
J. B. Fugate ◽  
L. Mohler
Keyword(s):  
Hausdorff Space ◽  
Disjoint Union ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
The One ◽  
One Point Compactification ◽  
Compact Subsets

It is well known (see [3](1)) that no continuum (i.e. compact, connected, Hausdorff space) can be written as a countable disjoint union of its (nonvoid) closed subsets. This result can be generalized in two ways into the setting of locally compact, connected, Hausdorff spaces. Using the one point compactification of a locally compact, connected, Hausdorff space X one can easily show that X cannot be written as a countable disjoint union of compact subsets. If one makes the further assumption that X is locally connected, then one can show that X cannot be written as a countable disjoint union of closed subsets.(2)

A Characterization of Compact Subsets of E1

1972 ◽  
Vol 79 (3) ◽  
pp. 278-279
Author(s):  
R. K. Tamaki
Keyword(s):  
Compact Subsets
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