共查询到20条相似文献,搜索用时 0 毫秒
1.
Yi Zhang 《Archive for Mathematical Logic》2000,39(1):41-52
We discuss the cardinalities of maximal cofinitary groups under the assumption of . We also discuss various open questions in this area.
Received: 24 July 1997 相似文献
2.
Václav Vlasák 《Topology and its Applications》2008,155(15):1672-1676
We investigate connections between complexity of a function f from a Polish space X to a Polish space Y and complexity of the set , where K(X) denotes the space of all compact subsets of X equipped with the Vietoris topology. We prove that if C(f) is analytic, then f is Borel; and assuming -determinacy we show that f is Borel if and only if C(f) is coanalytic. Similar results for projective classes are also presented. 相似文献
3.
Komjáth in 1984 proved that, for each sequence (An) of analytic subsets of a Polish space X, if lim supn∈HAn is uncountable for every H∈ω[N] then ?n∈GAn is uncountable for some G∈ω[N]. This fact, by our definition, means that the σ-ideal [X]?ω has property (LK). We prove that every σ-ideal generated by X/E has property (LK), for an equivalence relation E⊂X2 of type Fσ with uncountably many equivalence classes. We also show the parametric version of this result. Finally, the invariance of property (LK) with respect to various operations is studied. 相似文献
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5.
Tamás Mátrai 《Topology and its Applications》2010,157(8):1479-1484
We recall from [T. Mátrai, Kenilworth, Proc. Amer. Math. Soc. 137 (3) (2009) 1115-1125] a Gδσ-ideal of compact subsets of ω2 and prove that it is not Tukey reducible to the ideal . This result answers a question of S. Solecki and S. Todor?evi? in the negative. 相似文献
6.
Daisuke Ikegami 《Annals of Pure and Applied Logic》2010,161(7):879-894
For a large natural class of forcing notions, we prove general equivalence theorems between forcing absoluteness statements, regularity properties, and transcendence properties over and the core model . We use our results to answer open questions from set theory of the reals. 相似文献
7.
Hajnal and Juhász proved that under CH there is a hereditarily separable, hereditarily normal topological group without non-trivial convergent sequences that is countably compact and not Lindelöf. The example constructed is a topological subgroup H⊆ω12 that is an HFD with the following property
- (P)
- the projection of H onto every partial product I2 for I∈ω[ω1] is onto.
8.
We show the limits of Mackey's theorem applied to identity sets to prove that a given group has a unique Polish group topology.Verbal sets in Abelian Polish groups and full verbal sets in the infinite symmetric group are Borel. However this is not true in general.A Polish group with a neighborhood π-base at 1 of sets from the σ-algebra of identity and verbal sets has a unique Polish group topology. It follows that compact, connected, simple Lie groups, as well as finitely generated profinite groups, have a unique Polish group topology. 相似文献
9.
Chuan Liu 《Topology and its Applications》2012,159(5):1415-1420
We investigate some generalized metric space properties on paratopological (semitopological) groups and prove that a paratopological group that is quasi-metrizable by a left continuous, left-invariant quasi-metric is a topological group and give a negative answer to Ravsky?s question (Ravsky, 2001 [18, Question 3.1]). It is also shown that an uncountable paratopological group that is a closed image of a separable, locally compact metric space is a topological group. Finally, we discuss Hausdorff compactification of paratopological (semitopological) groups, give an affirmative answer to Lin and Shen?s question (Lin and Shen, 2011 [14, Question 6.9]) and improve an Arhangel?skii and Choban?s theorem. Some questions are posed. 相似文献
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11.
We construct a model of ZFC where every separable Fréchet topological group is metrizable. This solves a 1978 problem of V.I. Malykhin. 相似文献
12.
Piotr Zakrzewski 《Topology and its Applications》2008,155(13):1445-1449
We present new characterizations of universally meager sets, shown in [P. Zakrzewski, Universally meager sets, Proc. Amer. Math. Soc. 129 (6) (2001) 1793-1798] to be a category analog of universally null sets. In particular, we address the question of how this class is related to another class of universally meager sets, recently introduced by Todorcevic [S. Todorcevic, Universally meager sets and principles of generic continuity and selection in Banach spaces, Adv. Math. 208 (2007) 274-298]. 相似文献
13.
Taras Banakh Dušan Repovš Lyubomyr Zdomskyy 《Journal of Pure and Applied Algebra》2008,212(9):2105-2114
In this paper we answer the question of T. Banakh and M. Zarichnyi constructing a copy of the Fréchet-Urysohn fan Sω in a topological group G admitting a functorial embedding [0,1]⊂G. The latter means that each autohomeomorphism of [0,1] extends to a continuous homomorphism of G. This implies that many natural free topological group constructions (e.g. the constructions of the Markov free topological group, free abelian topological group, free totally bounded group, free compact group) applied to a Tychonov space X containing a topological copy of the space Q of rationals give topological groups containing Sω. 相似文献
14.
Yevhen Zelenyuk 《Topology and its Applications》2006,153(14):2382-2385
We introduce the notion of a partially selective ultrafilter and prove that (a) if G is an extremally disconnected topological group and p is a converging nonprincipal ultrafilter on G containing a countable discrete subset, then p is partially selective, and (b) the existence of a nonprincipal partially selective ultrafilter on a countable set implies the existence of a P-point in ω∗. Thus it is consistent with ZFC that there is no extremally disconnected topological group containing a countable discrete nonclosed subset. 相似文献
15.
Marion Scheepers 《Topology and its Applications》2011,158(13):1575-1583
We show that:
- (1)
- Rothberger bounded subgroups of σ-compact groups are characterized by Ramseyan partition relations (Corollary 4).
- (2)
- For each uncountable cardinal κ there is a T0 topological group of cardinality κ such that ONE has a winning strategy in the point-open game on the group and the group is not a closed subspace of any σ-compact space (Theorem 8).
- (3)
- For each uncountable cardinal κ there is a T0 topological group of cardinality κ such that ONE has a winning strategy in the point-open game on the group and the group is σ-compact (Corollary 17).
16.
We show that the existence of a non-metrizable compact subspace of a topological group G often implies that G contains an uncountable supersequence (a copy of the one-point compactification of an uncountable discrete space). The existence of uncountable supersequences in a topological group has a strong impact on bounded subsets of the group. For example, if a topological group G contains an uncountable supersequence and K is a closed bounded subset of G which does not contain uncountable supersequences, then any subset A of K is bounded in G?(K?A). We also show that every precompact Abelian topological group H can be embedded as a closed subgroup into a precompact Abelian topological group G such that H is bounded in G and all bounded subsets of the quotient group G/H are finite. This complements Ursul's result on closed embeddings of precompact groups to pseudocompact groups. 相似文献
17.
Nobuo Aoki 《Topology and its Applications》1985,20(1):1-15
It is proved, by using topological properties, that when a group automorphism of a locally compact totally disconnected group is ergodic under the Haar measure, the group is compact. The result is an answer for Halmos's question that has remained open for the totally disconnected case. 相似文献
18.
Marcin Szyszkowski 《Quaestiones Mathematicae》2018,41(2):165-171
We characterize sets A0, A1 for which there is a DB1 function f with [f = 0] = A0 and [f = 1] = A1. This characterization is a conjunction of necessary conditions for Darboux and for Baire 1 functions. We also characterize sets A?, A+ for which there is a DB1 function with [f < 0] = A? and [f > 0] = A+. The same characterzations are provided for approximately continuous functions. 相似文献
19.
A Hausdorff topological group G is minimal if every continuous isomorphism f:G→H between G and a Hausdorff topological group H is open. Significantly strengthening a 1981 result of Stoyanov, we prove the following theorem: For every infinite minimal abelian group G there exists a sequence of cardinals such that
20.
W. Adamski 《Periodica Mathematica Hungarica》1990,21(2):85-93
By considering two exemplary situations, it is shown that only under rather restrictive assumptions it is, in general, possible to derive properties of the underlying topology from properties of the associated Baire and Borel -algebra, respectively. 相似文献