摘要:

ABSTRACT.Some bounds on the cardinality of LindelöfT1‐spaces such that small subspaces verify a meta‐Lindelöf property are proved. A procedure to extend these results to a larger class of spaces is

ISSN:0077-8923    

DOI:10.1111/j.1749-6632.1993.tb52503.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

ABSTRACT.H‐enrichments of topologies are larger (i.e., inclusive) topologies that also have larger homeomorphism groups. The study ofH‐enrichments of the Euclidean and rational topologies via generalized Baire category arguments is continued. New results concern lower bounds on the number ofH‐enrichments, connectedness, and separation properties of such topologies and certain of their cardinal invar

ISSN:0077-8923    

DOI:10.1111/j.1749-6632.1993.tb52504.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

ABSTRACT.A compactificationkRnof Rnis geometric if (a) the closure inkRnof every closed topological copy of Rn‐1separateskRn, and (b) any two points inkRncan be separated by the closure of such a topological hyperplane. The first condition trivially holds ifkRnis a perfect compactification. Preliminary relationships between these two properties are discussed. The closedn‐ballBnwithSn‐1as remainder andkRnare geometric compactifications, as is any perfect metrizable compactification of R2with nondegenerate remainder. The property of being geometric seems to be rare among compactifications of Rn, and it is surprising that it is shared by two as different asBn

ISSN:0077-8923    

DOI:10.1111/j.1749-6632.1993.tb52505.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

ABSTRACT.Those uniform spaces whose uniform hyperspaces are locally compact are characterized. Some properties of the set of points of local compactness of a uniform hyperspace are investigated.

ISSN:0077-8923    

DOI:10.1111/j.1749-6632.1993.tb52506.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

ABSTRACT.The current state of knowledge concerning liftings for noncomplete probability spaces is discussed. This is a somewhat expanded version of the author's talk given at the 1991 Summer Conference on General Topology and Applications in Honor of Mary Ellen Rudin and Her Work.

ISSN:0077-8923    

DOI:10.1111/j.1749-6632.1993.tb52507.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

ABSTRACT.Basic results are obtained concerning Galois connections between collections of closure operators (of various types) and collections consisting of subclasses of (pairs of) morphisms in

ISSN:0077-8923    

DOI:10.1111/j.1749-6632.1993.tb52508.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

ABSTRACT.A range of topologies, generated in a “preuniform” manner, is shown to give conditions for a space to be (1) Nagata over a regular infinite cardinal α, and (2) α‐metrizable. Connections with the structuring mechanism introduced by P. J. Collins and A. W. Roscoe are investigated. The metrizability degree of a regular space is shown to be equal to the minimum among cardinals arising as weights of compatible local uniformities, and the reader is asked to characterize topologies admitting monotonic quasi uniformities. Various relevant cardinal invariants are discussed; in particular, comparisons are made involving the transitivity and γ

ISSN:0077-8923    

DOI:10.1111/j.1749-6632.1993.tb52509.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

ABSTRACT.THEOREM. The topological partition relation ω*→ (Y)12(a) Fails for every spaceYwith |Y| |Mg 2c;(b) Holds forYdiscrete if and only if |Y| |Ml c;(c) Holds for certain nondiscrete P‐spacesY;(d) Fails forY=ω Imu {p} withp∉ω*;(e) Fails forYinfinite and countably

ISSN:0077-8923    

DOI:10.1111/j.1749-6632.1993.tb52510.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

ABSTRACT.The relationships holding between integral summability methods, certain set functions defined on ℘ ([0, ∞)), and certain closed subsets of β[0, ∞) ‐ [0, ∞) have been discussed before. In this paper some of these results are extended to more general topological spaces. For a locally compact Tychonoff spaceX, relationships between set functions on ℘ (X), certain closed subsets of βX ‐X, and ideals ofC*(X) are given, as are applications to sum

ISSN:0077-8923    

DOI:10.1111/j.1749-6632.1993.tb52511.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY

摘要:

ABSTRACT.Two countable spaces having no nontrivial convergent sequences are constructed. One space has every point biaccessible (by a countable discrete set), and the other has every point accessible but not biaccessible (by a countable discrete set). It is shown that in a compactT2‐space if a setAis not closed, then there exists a free sequence contained inAwhose closure is not contained inA. It follows that in a compactT2‐space of countable tightness, every nonisolated point is biaccessi

ISSN:0077-8923    

DOI:10.1111/j.1749-6632.1993.tb52512.x

出版商:Blackwell Publishing Ltd    

年代:1993

数据来源: WILEY