共查询到20条相似文献,搜索用时 15 毫秒
1.
Kyriakos Kermedis 《Mathematical Logic Quarterly》2003,49(4):369-374
We show that the statement (K12) “separable, countably compact, regular spaces are Baire” is deducible from a strictly weaker form than AC, namely, CAC(?) (the axiom of choice for countable families of non‐empty subsets of the real line ?). We also find some characterizations of the axiom of dependent choices. 相似文献
2.
Keita Yokoyama 《Archive for Mathematical Logic》2007,46(1):15-35
This research is motivated by the program of Reverse Mathematics. We investigate basic part of complex analysis within some weak subsystems of second order arithmetic, in order to determine what kind of set existence axioms are needed to prove theorems of basic analysis. We are especially concerned with Cauchy’s integral theorem. We show that a weak version of Cauchy’s integral theorem is proved in RCAo. Using this, we can prove that holomorphic functions are analytic in RCAo. On the other hand, we show that a full version of Cauchy’s integral theorem cannot be proved in RCAo but is equivalent to weak König’s lemma over RCAo. 相似文献
3.
Let X be a locally compact metric space. One important object connected with the distribution behavior of an arbitrary sequence x on X is the set M( x ) of limit measures of x . It is defined as the set of accumulation points of the sequence of the discrete measures induced by x . Using binary representation of reals one gets a natural bijective correspondence between infinite subsets of the set ℕ of positive integers and numbers in the unit interval I = 〈0, 1]. Hence to each sequence x = (xn)n∈ℕ ∈ Xℕ and every a I there corresponds a subsequence denoted by a x . We investigate the set M(a x ) for given x with emphasis on the behavior for “typical” a in the sense of Baire category, Lebesgue measure and Hausdorff dimension. 相似文献
4.
本文讨论了由(?)-smooth拓扑分子格和(?)-smooth连续的广义序同态所构成的STML((?)) 范畴的若干结果,证明了范畴STML((?))是拓扑范畴,范畴TML是范畴STML((?))的双反射满子范畴,以及两个伴随定理. 相似文献
5.
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
6.
In this paper, we show within ${\mathsf{RCA}_0}In this paper, we show within that both the Jordan curve theorem and the Sch?nflies theorem are equivalent to weak K?nig’s lemma. Within , we prove the Jordan curve theorem using an argument of non-standard analysis based on the fact that every countable non-standard
model of has a proper initial part that is isomorphic to itself (Tanaka in Math Logic Q 43:396–400, 1997).
相似文献
7.
8.
Takako Nemoto MedYahya Ould MedSalem Kazuyuki Tanaka 《Mathematical Logic Quarterly》2007,53(3):226-236
In this paper we study the determinacy strength of infinite games in the Cantor space and compare them with their counterparts in the Baire space. We show the following theorems: 1. RCA0 ? ‐Det* ? ‐Det* ? WKL0. 2. RCA0 ? ( )2‐Det* ? ACA0. 3. RCA0 ? ‐Det* ? ‐Det* ? ‐Det ? ‐Det ? ATR0. 4. For 1 < k < ω, RCA0 ? ( )k ‐Det* ? ( )k –1‐Det. 5. RCA0 ? ‐Det* ? ‐Det. Here, Det* (respectively Det) stands for the determinacy of infinite games in the Cantor space (respectively the Baire space), and ( )k is the collection of formulas built from formulas by applying the difference operator k – 1 times. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
9.
10.
In this paper we define certain types of projections of planar sets and study some properties of such projections. 相似文献
11.
Chang-Kwon Choi 《Indagationes Mathematicae》2019,30(1):240-249
Let be a real normed vector space and . In this paper, we prove the hyperstability of the logarithmic functional equation on of Lebesgue measure zero. More precisely, we prove that if satisfies for all of Lebesgue measure zero, where is an arbitrary given function and satisfies the condition as [resp. ], then satisfies the functional equation for all and. 相似文献
12.
13.
14.
《Annals of Pure and Applied Logic》2014,165(2):520-551
In this paper, we introduce systems of nonstandard second-order arithmetic which are conservative extensions of systems of second-order arithmetic. Within these systems, we do reverse mathematics for nonstandard analysis, and we can import techniques of nonstandard analysis into analysis in weak systems of second-order arithmetic. Then, we apply nonstandard techniques to a version of Riemannʼs mapping theorem, and show several different versions of Riemannʼs mapping theorem. 相似文献
15.
Throughout this paper R denotes the set of all real numbers.An extended real valued function j f X-[--oo, +oc] is called lower semicontinuouson X if fOr each real Q, {x' f(x) > o} is open in X. Clearly, f is lower semicontinuous ifand only if, its epigraph eghf = {(x, a) f f(x) 5 cr} is closed in X x R. f is caJ1ed proper ifit is somewhere finite, and its values lie in (--co, +oc]. We denote by LSC(X) the set of ajlproper lower semicontinuous functions.In the sequel, we identify lower se… 相似文献
16.
17.
Philippe Moser 《Mathematical Logic Quarterly》2010,56(5):461-469
This paper studies how well computable functions can be approximated by their Fourier series. To this end, we equip the space of Lp‐computable functions (computable Lebesgue integrable functions) with a size notion, by introducing Lp‐computable Baire categories. We show that Lp‐computable Baire categories satisfy the following three basic properties. Singleton sets {f } (where f is Lp‐computable) are meager, suitable infinite unions of meager sets are meager, and the whole space of Lp‐computable functions is not meager. We give an alternative characterization of meager sets via Banach‐Mazur games. We study the convergence of Fourier series for Lp‐computable functions and show that whereas for every p > 1, the Fourier series of every Lp‐computable function f converges to f in the Lp norm, the set of L1‐computable functions whose Fourier series does not diverge almost everywhere is meager (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
18.
葛斌华 《数学的实践与认识》2001,31(3):374-376
从单位圆到以光滑 Jordan曲线为边界的单连通区域的共形映射 ,其边界的光滑性有经典的Kellogg定理及其推广的 Warschawski定理 ,本文以连续模、P次平均模为工具对原结果进行了深入的讨论 ,得到了更为一般的结果 . 相似文献
19.
Keita Yokoyama 《Mathematical Logic Quarterly》2007,53(2):132-146
This research is motivated by the program of reverse mathematics and non‐standard arguments in second‐order arithmetic. Within a weak subsystem of second‐order arithmetic ACA0, we investigate some aspects of non‐standard analysis related to sequential compactness. Then, using arguments of non‐standard analysis, we show the equivalence of the Riemann mapping theorem and ACA0 over WKL0. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
20.
We define and investigate some new ideals of subsets of the Cantor space and the Baire space. We show that combinatorial properties of these ideals can be described by the splitting and reaping cardinal numbers. We show that there exist perfect Luzin sets for these ideals on the Baire space.