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21.
Jacek Cichon Andrzej Jasinski Anastasis Kamburelis Przemyslaw Szczepaniak 《Proceedings of the American Mathematical Society》2002,130(6):1833-1842
In this paper we discuss various questions connected with translations of subsets of the real line. Most of these questions originate from W. Sierpinski. We discuss the number of translations a single subset of the reals may have. Later we discuss almost invariant subsets of Abelian groups.
22.
A subset of the -dimensional torus is called a set of uniqueness, or -set, if every multiple trigonometric series spherically converging to outside vanishes identically. We show that all countable sets are -sets and also that sets are -sets for every . In particular, , where is the Cantor set, is an set and hence a -set. We will say that is a -set if every multiple trigonometric series spherically Abel summable to outside and having certain growth restrictions on its coefficients vanishes identically. The above-mentioned results hold also for sets. In addition, every -set has measure , and a countable union of closed -sets is a -set.
23.
David L. Fearnley 《Proceedings of the American Mathematical Society》1999,127(10):3095-3100
The author answers a question raised in the literature about twenty five years ago and raised again more recently in Open Problems in Topology, by G. M. Reed, concerning the conjecture that every Moore space with a -discrete -base can be densely embedded in a Moore space having the Baire property. Even though closely related results have made this conjecture seem likely to be true, the author shows that, surprisingly, the conjecture is false.
24.
Dongyuan Yao 《K-Theory》1996,10(3):307-322
Let A be an Abelian category and B be a thick subcategory of A. Let D
b(B) denote the derived category of cohomologically bounded chain complexes of objects in A and D
B
b
(A) denote the derived category of cohomologically bounded chain complexes of objects in A with cohomology in B. We give two if and only if conditions for equivalence of D(B) and D
B
b
(A), and we give an example where D
b
(B) and D
B
b
(A) are not equivalent. 相似文献
25.
We develop a notion of an n-fold monoidal category and show that it corresponds in a precise way to the notion of an n-fold loop space. Specifically, the group completion of the nerve of such a category is an n-fold loop space, and free n-fold monoidal categories give rise to a finite simplicial operad of the same homotopy type as the classical little cubes operad used to parametrize the higher H-space structure of an n-fold loop space. We also show directly that this operad has the same homotopy type as the n-th Smith filtration of the Barratt-Eccles operad and the n-th filtration of Berger's complete graph operad. Moreover, this operad contains an equivalent preoperad which gives rise to Milgram's small model for when n=2 and is very closely related to Milgram's model of for n>2. 相似文献
26.
Ralph Kummetz 《Applied Categorical Structures》2003,11(1):3-25
This paper investigates function spaces of structures consisting of a partially ordered set together with some directed family of projections.More precisely, given a fixed directed index set (I,), we consider triples (D,,(p
i
)
iI
) with (D,) a poset and (p
i
)
iI
a monotone net of projections of D. We call them (I,)-pop's (posets with projections). Our main purpose is to study structure preserving maps between (I,)-pop's. Such homomorphisms respect both order and projections.Any (I,)-pop is known to induce a uniformity and thus a topology. The set of all homomorphisms between two (I,)-pop's turns out to form an (I,)-pop itself. We show that its uniformity is the uniformity of uniform convergence. This enables us to prove that properties such as completeness and compactness transfer to function pop's.Concerning categorical properties of (I,)-pop's, we will see that we are in a lucky situation from a computer scientist's point of view: we obtain Cartesian closed categories. Moreover, by a D
-construction we get (I,)-pop's that are isomorphic to their own exponent. This yields new models for the untyped -calculus. 相似文献
27.
Má rton Elekes Kenneth Kunen 《Proceedings of the American Mathematical Society》2003,131(8):2453-2457
The set of continuous or Baire class 1 functions defined on a metric space is endowed with the natural pointwise partial order. We investigate how the possible lengths of well-ordered monotone sequences (with respect to this order) depend on the space .
28.
Michel Hébert 《Applied Categorical Structures》2001,9(6):595-623
We give concrete versions of the characterizations of locally -presentable (resp. -generated) categories as categories of models of (resp. weakly) -ary limit-theories and of (resp. weakly) -ary essentially algebraic theories. By concrete we mean that starting with a category of -structures, the theories obtained are extensions of the original ones, and the equivalences of categories are concrete isomorphisms. -presentable and -generated objects are also investigated from this viewpoint. 相似文献
29.
Piotr Zakrzewski 《Proceedings of the American Mathematical Society》2001,129(6):1793-1798
We study category counterparts of the notion of a universal measure zero set of reals.
We say that a set is universally meager if every Borel isomorphic image of is meager in . We give various equivalent definitions emphasizing analogies with the universally null sets of reals.
In particular, two problems emerging from an earlier work of Grzegorek are solved.
30.
We prove that (a) in a reflexive space, for any linearly bounded but unbounded closed convex subset the nonsupport functionals are a dense G
subset of the polar set, and (b) any nonsemicoercive proper convex lsc [weak*-lsc] function in a [dual] Banach space has a generic [dense G
] set of L
-perturbations which do not attain their infimum. We also characterize the proper convex functions that have inf-nonattaining L
-perturbations. This results also in a criterion for reflexivity. 相似文献