共查询到20条相似文献,搜索用时 15 毫秒
1.
W. F. Lindgren A. A. Szymanski 《Proceedings of the American Mathematical Society》1997,125(12):3741-3746
We show that under Martin's axiom there are spaces which are countably compact extremally disconnected homogeneous such that the product of any two them is not pseudocompact. The spaces are modeled on the space Seq().
2.
Mary Ellen Rudin Ian S. Stares Jerry E. Vaughan 《Proceedings of the American Mathematical Society》1997,125(3):927-934
We show that every countably compact space which is monotonically normal, almost 2-fully normal, radial , or with countable spread is absolutely countably compact. For the first two mentioned properties, we prove more general results not requiring countable compactness. We also prove that every monotonically normal, orthocompact space is finitely fully normal.
3.
Raushan Z. Buzyakova 《Topology and its Applications》2010,157(14):2289-161
We show that if X is countably compact but not compact then one can find a compact space K such that X⊕K does not embed closedly into any normal topological group. 相似文献
4.
Dikran Dikranjan Michael Tkachenko 《Proceedings of the American Mathematical Society》2002,130(8):2487-2496
We prove under the assumption of Martin's Axiom that every precompact Abelian group of size belongs to the smallest class of groups that contains all Abelian countably compact groups and is closed under direct products, taking closed subgroups and continuous isomorphic images.
5.
Artur Hideyuki Tomita 《Topology and its Applications》2005,150(1-3):197-205
We show the existence of a p-compact group whose size has countable cofinality in a forcing model. As a corollary, we show that consistently there exists a countably compact group whose size has countable cofinality and its weight is larger than the size. 相似文献
6.
We obtain (a) necessary and sufficient conditions and (b) sufficient conditions for a compact (countably compact) set to be closed in products (sequential products) and subspaces (sequential subspaces) of normal spaces. As a consequence of these, sufficient conditions are obtained for (i) the closedness of arbitrary (countable) union of closed sets and (ii) the equality of the union of the closures and the closure of the union of arbitrary (countable) families of sets in these spaces. It is also shown that these results do not hold for quotients of even T
4,-spaces. 相似文献
7.
Desmond Robbie Sergey Svetlichny 《Proceedings of the American Mathematical Society》1996,124(1):325-330
It is shown under CH that there exists a countably compact topological semigroup with two-sided cancellation which is not a topological group. Wallace's question" of 40 years standing is thus settled in the negative unless CH is explicitly denied. The example is a topological subsemigroup of an uncountable product of circle groups.
8.
It is well known that some classes of spaces such as absolutely countably compact (abbreviated acc) spaces and (a)-spaces are not hereditary with respect to closed, and even regular closed subspaces. In this paper, we investigate conditions for spaces being regular closed embeddable into spaces with certain covering properties, in particular we characterize spaces which can be embedded as regular closed subsets into acc spaces and (a)-spaces. Some examples are presented as applications of the criteria. Two problems raised by Matveev [Topology Appl. 80 (1997) 169–175] are answered. 相似文献
9.
10.
Comfort and Remus [W.W. Comfort, D. Remus, Abelian torsion groups with a pseudocompact group topology, Forum Math. 6 (3) (1994) 323–337] characterized algebraically the Abelian torsion groups that admit a pseudocompact group topology using the Ulm–Kaplansky invariants.We show, under a condition weaker than the Generalized Continuum Hypothesis, that an Abelian torsion group (of any cardinality) admits a pseudocompact group topology if and only if it admits a countably compact group topology. Dikranjan and Tkachenko [D. Dikranjan, M. Tkachenko, Algebraic structure of small countably compact Abelian groups, Forum Math. 15 (6) (2003) 811–837], and Dikranjan and Shakhmatov [D. Dikranjan, D. Shakhmatov, Forcing hereditarily separable compact-like group topologies on Abelian groups, Topology Appl. 151 (1–3) (2005) 2–54] showed this equivalence for groups of cardinality not greater than .We also show, from the existence of a selective ultrafilter, that there are countably compact groups without non-trivial convergent sequences of cardinality κω, for any infinite cardinal κ. In particular, it is consistent that for every cardinal κ there are countably compact groups without non-trivial convergent sequences whose weight λ has countable cofinality and λ>κ. 相似文献
11.
Mohammad Ismail 《Topology and its Applications》1980,11(3):281-292
A space X is called C-closed if every countably compact subset of X is closed in X. We study the properties of C-closed spaces. Among other results, it is shown that countably compact C-closed spaces have countable tightness and under Martin's Axiom or 2ω0<2ω1, C-closed is equivalent to sequential for compact Hausdorff spaces. Furthermore, every hereditarily quasi-k Hausdorff space is Fréchet-Urysohn, which generalizes a theorem of Arhangel'sk
in [4]. Also every hereditarily q-space is hereditarily of pointwise countable type and contains an open dense first countable subspace. 相似文献
12.
In this paper, the notion of the bounded compact approximation property (BCAP) of a pair [Banach space and its subspace] is used to prove that if X is a closed subspace of L∞ with the BCAP, then L∞/X has the BCAP. We also show that X* has the λ-BCAP with conjugate operators if and only if the pair (X, Y) has the λ-BCAP for each finite codimensional subspace Y∈X. Let M be a closed subspace of X such that M⊥ is complemented in X*. If X has the (bounded) approximation property of order p, then M has the (bounded) approximation property of order p. 相似文献
13.
We give an example of a -normal space which is not densely normal.
14.
A small Dowker space in ZFC 总被引:1,自引:0,他引:1
Zoltan T. Balogh 《Proceedings of the American Mathematical Society》1996,124(8):2555-2560
We construct a hereditarily normal topological space whose product with the unit interval is not normal. The space is -relatively discrete and has cardinality of the continuum .
15.
Wieslaw Kubis Vladimir Uspenskij 《Proceedings of the American Mathematical Society》2005,133(8):2483-2487
A compact space is Valdivia compact if it can be embedded in a Tikhonov cube in such a way that the intersection is dense in , where is the sigma-product ( the set of points with countably many non-zero coordinates). We show that there exists a compact connected Abelian group of weight which is not Valdivia compact, and deduce that Valdivia compact spaces are not preserved by open maps.
16.
We construct a pseudocompact meta-Lindelöf space which is not compact. This contrasts with the results that pseudocompact metacompact spaces are compact (Scott, Forster, Watson) and that pseudocompact para-Lindelöf spaces are compact (Burke, Davis). The space is completely regular and has a point-countable base. 相似文献
17.
Artur Hideyuki Tomita 《Proceedings of the American Mathematical Society》2003,131(8):2617-2622
E. K. van Douwen asked in 1980 whether the cardinality of a countably compact group must have uncountable cofinality in . He had shown that this was true under GCH. We answer his question in the negative. V. I. Malykhin and L. B. Shapiro showed in 1985 that under GCH the weight of a pseudocompact group without non-trivial convergent sequences cannot have countable cofinality and showed that there is a forcing model in which there exists a pseudocompact group without non-trivial convergent sequences whose weight is . We show that it is consistent that there exists a countably compact group without non-trivial convergent sequences whose weight is .
18.
Henno Brandsma Jan van Mill 《Proceedings of the American Mathematical Society》1998,126(11):3407-3411
We show that Kunen's example of a compact L-space, constructed under CH, can be modified so that it has a non-monolithic hyperspace. This answers a question of Bell's. This example is also relevant to a question of Arhangel'skii's.
19.
Vladimir P. Fonf Clemente Zanco 《Proceedings of the American Mathematical Society》2006,134(9):2607-2611
A well-known theorem by H. Corson states that if a Banach space admits a locally finite covering by bounded closed convex subsets, then it contains no infinite-dimensional reflexive subspace. We strengthen this result proving that if an infinite-dimensional Banach space admits a locally finite covering by bounded -closed subsets, then it is -saturated, thus answering a question posed by V. Klee concerning locally finite coverings of spaces. Moreover, we provide information about massiveness of the set of singular points in (PC) spaces.
20.
Alexandre I. Danilenko Andres del Junco 《Proceedings of the American Mathematical Society》2008,136(7):2463-2472
Via the cut-and-stack construction we produce a 2-fold simple weakly mixing transformation which has countably many proper factors and all of them are 2-to-1 and prime.