A NOTE ON SPACES WITH A STRONG RANK 1-DIAGONAL

2013 ◽  
Vol 89 (3) ◽  
pp. 510-513
Author(s):  
WEI-FENG XUAN ◽  
WEI-XUE SHI
Keyword(s):  
Compact Space ◽  
Star Compact

AbstractWe mainly prove that, assuming $\mathfrak{b}= \mathfrak{c}$, every regular star-compact space with a strong rank 1-diagonal is metrisable.

scholarly journals AN ANSWER TO VAN MILL’S QUESTION

2008 ◽  
Vol 78 (3) ◽  
pp. 353-355 ◽  
Author(s):  
ER-GUANG YANG ◽  
WEI-XUE SHI
Keyword(s):  
Compact Space ◽  
Negative Answer ◽  
Star Compact

Abstractvan Mill et al. posed in ‘Classes defined by stars and neighborhood assignments’, Topology Appl.154 (2007), 2127–2134 the following question: Is a star-compact space metrizable if it has a Gδ-diagonal? In this paper, we give a negative answer to this question.

scholarly journals A NOTE ON STAR COMPACT SPACES WITH POINT-COUNTABLE BASE

2010 ◽  
Vol 81 (3) ◽  
pp. 493-495
Author(s):  
YAN-KUI SONG
Keyword(s):  
Compact Space ◽  
Countable Base ◽  
Compact Spaces ◽  
Star Compact

AbstractIn this note we give an example of a Hausdorff, star compact space with point-countable base which is not metrizable.

scholarly journals A dichotomy for bounded displacement equivalence of Delone sets

2021 ◽  
pp. 1-18
Author(s):  
YOTAM SMILANSKY ◽  
YAAR SOLOMON
Keyword(s):  
Compact Space ◽  
Equivalence Classes ◽  
Natural Topology ◽  
Fell Topology ◽  
Local Complexity ◽  
Substitution Tilings ◽  
Local Topology ◽  
Delone Sets

Abstract We prove that in every compact space of Delone sets in ${\mathbb {R}}^d$ , which is minimal with respect to the action by translations, either all Delone sets are uniformly spread or continuously many distinct bounded displacement equivalence classes are represented, none of which contains a lattice. The implied limits are taken with respect to the Chabauty–Fell topology, which is the natural topology on the space of closed subsets of ${\mathbb {R}}^d$ . This topology coincides with the standard local topology in the finite local complexity setting, and it follows that the dichotomy holds for all minimal spaces of Delone sets associated with well-studied constructions such as cut-and-project sets and substitution tilings, whether or not finite local complexity is assumed.

scholarly journals Schwinger effect in compact space

2021 ◽  
Vol 103 (12) ◽  
Author(s):  
Prasant Samantray ◽  
Suprit Singh
Keyword(s):  
Compact Space ◽  
Schwinger Effect

scholarly journals THE POLYNOMIAL NUMERICAL INDEX OF A BANACH SPACE

2006 ◽  
Vol 49 (1) ◽  
pp. 39-52 ◽  
Author(s):  
Yun Sung Choi ◽  
Domingo Garcia ◽  
Sung Guen Kim ◽  
Manuel Maestre
Keyword(s):  
Banach Space ◽  
Positive Integer ◽  
Banach Spaces ◽  
Compact Space ◽  
Linear Operators ◽  
Homogeneous Polynomials ◽  
Numerical Radius ◽  
Disc Algebra ◽  
Multilinear Maps ◽  
Numerical Index

AbstractIn this paper, we introduce the polynomial numerical index of order $k$ of a Banach space, generalizing to $k$-homogeneous polynomials the ‘classical’ numerical index defined by Lumer in the 1970s for linear operators. We also prove some results. Let $k$ be a positive integer. We then have the following:(i) $n^{(k)}(C(K))=1$ for every scattered compact space $K$.(ii) The inequality $n^{(k)}(E)\geq k^{k/(1-k)}$ for every complex Banach space $E$ and the constant $k^{k/(1-k)}$ is sharp.(iii) The inequalities$$ n^{(k)}(E)\leq n^{(k-1)}(E)\leq\frac{k^{(k+(1/(k-1)))}}{(k-1)^{k-1}}n^{(k)}(E) $$for every Banach space $E$.(iv) The relation between the polynomial numerical index of $c_0$, $l_1$, $l_{\infty}$ sums of Banach spaces and the infimum of the polynomial numerical indices of them.(v) The relation between the polynomial numerical index of the space $C(K,E)$ and the polynomial numerical index of $E$.(vi) The inequality $n^{(k)}(E^{**})\leq n^{(k)}(E)$ for every Banach space $E$.Finally, some results about the numerical radius of multilinear maps and homogeneous polynomials on $C(K)$ and the disc algebra are given.

Conformal invariance and string theory in compact space: Bosons

1985 ◽  
Vol 32 (10) ◽  
pp. 2713-2721 ◽  
Author(s):  
Sanjay Jain ◽  
R. Shankar ◽  
Spenta R. Wadia
Keyword(s):  
String Theory ◽  
Compact Space ◽  
Conformal Invariance
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