scholarly journals Local compactness and cartesian products of quotient maps and $K$-spaces

1968 ◽  
Vol 18 (2) ◽  
pp. 281-286 ◽  
Author(s):  
Ernest Michael
Keyword(s):  
Cartesian Products ◽  
Local Compactness ◽  
Quotient Maps

scholarly journals Peg Solitaire on Cartesian Products of Graphs

2021 ◽  
Vol 37 (3) ◽  
pp. 907-917
Author(s):  
Martin Kreh ◽  
Jan-Hendrik de Wiljes
Keyword(s):  
Cartesian Product ◽  
Cartesian Products ◽  
Connected Graphs ◽  
Grid Graphs ◽  
Cartesian Products Of Graphs

AbstractIn 2011, Beeler and Hoilman generalized the game of peg solitaire to arbitrary connected graphs. In the same article, the authors proved some results on the solvability of Cartesian products, given solvable or distance 2-solvable graphs. We extend these results to Cartesian products of certain unsolvable graphs. In particular, we prove that ladders and grid graphs are solvable and, further, even the Cartesian product of two stars, which in a sense are the “most” unsolvable graphs.

On topological quotient maps preserved by pullbacks or products

1970 ◽  
Vol 67 (3) ◽  
pp. 553-558 ◽  
Author(s):  
B. J. Day ◽  
G. M. Kelly
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Quotient Maps ◽  
Continuous Maps

We are concerned with the category of topological spaces and continuous maps. A surjection f: X → Y in this category is called a quotient map if G is open in Y whenever f−1G is open in X. Our purpose is to answer the following three questions:Question 1. For which continuous surjections f: X → Y is every pullback of f a quotient map?Question 2. For which continuous surjections f: X → Y is f × lz: X × Z → Y × Z a quotient map for every topological space Z? (These include all those f answering to Question 1, since f × lz is the pullback of f by the projection map Y ×Z → Y.)Question 3. For which topological spaces Z is f × 1Z: X × Z → Y × Z a qiptoent map for every quotient map f?

scholarly journals The distinguishing number of Cartesian products of complete graphs

2008 ◽  
Vol 29 (4) ◽  
pp. 922-929 ◽  
Author(s):  
Wilfried Imrich ◽  
Janja Jerebic ◽  
Sandi Klavžar
Keyword(s):  
Complete Graphs ◽  
Cartesian Products ◽  
Distinguishing Number

scholarly journals Local compactness in approach spaces II

2003 ◽  
Vol 2003 (2) ◽  
pp. 109-117
Author(s):  
R. Lowen ◽  
C. Verbeeck
Keyword(s):  
Stability Properties ◽  
Local Compactness ◽  
The Stability ◽  
Approach Spaces

This paper studies the stability properties of the concepts of local compactness introduced by the authors in 1998. We show that all of these concepts are stable for contractive, expansive images and for products.

scholarly journals On the maximal Sobolev regularity of distributions supported by subsets of Euclidean space

2016 ◽  
Vol 15 (05) ◽  
pp. 731-770 ◽  
Author(s):  
D. P. Hewett ◽  
A. Moiola
Keyword(s):  
Maximal Regularity ◽  
Cantor Sets ◽  
Characteristic Functions ◽  
Bessel Potential ◽  
Empty Interior ◽  
Cartesian Products ◽  
Sobolev Regularity ◽  
Full Classification ◽  
Differential And Integral Equations

This paper concerns the following question: given a subset [Formula: see text] of [Formula: see text] with empty interior and an integrability parameter [Formula: see text], what is the maximal regularity [Formula: see text] for which there exists a non-zero distribution in the Bessel potential Sobolev space [Formula: see text] that is supported in [Formula: see text]? For sets of zero Lebesgue measure, we apply well-known results on set capacities from potential theory to characterize the maximal regularity in terms of the Hausdorff dimension of [Formula: see text], sharpening previous results. Furthermore, we provide a full classification of all possible maximal regularities, as functions of [Formula: see text], together with the sets of values of [Formula: see text] for which the maximal regularity is attained, and construct concrete examples for each case. Regarding sets with positive measure, for which the maximal regularity is non-negative, we present new lower bounds on the maximal Sobolev regularity supported by certain fat Cantor sets, which we obtain both by capacity-theoretic arguments, and by direct estimation of the Sobolev norms of characteristic functions. We collect several results characterizing the regularity that can be achieved on certain special classes of sets, such as [Formula: see text]-sets, boundaries of open sets, and Cartesian products, of relevance for applications in differential and integral equations.

scholarly journals THE FERMION DOUBLING PROBLEM AND NONCOMMUTATIVE GEOMETRY

2000 ◽  
Vol 15 (19) ◽  
pp. 1279-1286 ◽  
Author(s):  
A. P. BALACHANDRAN ◽  
T. R. GOVINDARAJAN ◽  
B. YDRI
Keyword(s):  
Noncommutative Geometry ◽  
Field Theories ◽  
Fuzzy Sphere ◽  
Cartesian Products

We propose a resolution for the fermion doubling problem in discrete field theories based on the fuzzy sphere and its Cartesian products. Its relation to the Ginsparg–Wilson approach is also clarified.

Decycling Cartesian Products of Two Cycles

2005 ◽  
Vol 19 (3) ◽  
pp. 651-663 ◽  
Author(s):  
David A. Pike ◽  
Yubo Zou
Keyword(s):  
Cartesian Products

The Existence of Certain Partitions on Cartesian Products

1978 ◽  
Vol 24 (19-24) ◽  
pp. 325-333 ◽  
Author(s):  
Allan W. Ristow
Keyword(s):  
Cartesian Products
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