摘要:

An explicit description of the finest splitting uniformity is developed by regarding the categoryUnifof uniform spaces and uniformly continuous maps as a subcategory of the categoryUConof uniform convergence spaces, and then applying some general categorical results concerning Cartesian closedness. Also given (and required by this procedure) are explicit descriptions of final structures inUCon, and of the objects of the coreflective hull ofUnifinUCon.

ISSN:0077-8923    

DOI:10.1111/j.1749-6632.1992.tb32241.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Some characterizations of the conjugate of a Banach–Stone mapT : C(X) → C(Y)between the non–Archimedean spaces of continuous functionsC(X)andC(Y)are studied. The main result thatT′ : C(Y)′→ C(X)′is a Banach–Stone map if and only ifTis a Banach–St

ISSN:0077-8923    

DOI:10.1111/j.1749-6632.1992.tb32242.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

A spaceXis said to be cleavable over a spaceYif for every subsetAofXthere exists a continuous mappingf : X → Ysuch thatA = f−1f(A). It is shown that a compact spaceXis cleavable over the spaceRof real numbers if and only ifXis homeomorphic to a subspace ofR. It is also proved that if a spaceXis cleavable overRn, wherenis a natural number, andVis a subspace ofXhomeomorphic toRn, thenVis open inX. Every infinite connected subset of any space cleavable overRis shown to have a nonempty inter

ISSN:0077-8923    

DOI:10.1111/j.1749-6632.1992.tb32243.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

ISSN:0077-8923    

DOI:10.1111/j.1749-6632.1992.tb32244.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Results obtained by and with Dieter Remus are recapitulated and advanced as follows: IfGis an Abelian group or a free group, and if |G|=γ≥ω, thenGhas 22γ‐many Hausdorff topological group topologies that are totally bounded, and an equal number that are not; each class contains an antichain of cardinality 22γ, and each class contains a chain of length β iff the power set ?(γ), partially ordered under inclusion, admits a chain of length β.As to pseudocompact group topologies, the groups ⊕γQserve as test spaces in this sense: If some groupGwith |G|=γ≥ω has a pseudocompact group topology of weight α, then so does ⊕γQ; in case theP‐space topology of {0, 1}αhas density character (log α)ω(as is the case if the singular cardinals hypothesis is assumed), then the free Abelian group ⊕γZis also a test space when α>ω.Severa

ISSN:0077-8923    

DOI:10.1111/j.1749-6632.1992.tb32245.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

Let ℵ be an infinite cardinal number and ℛ (ℵ, 1) a complete metric space of density ℵ and uniform dimension 1 uniformly universal in the class of all metric spaces of density ≤ℵ and uniform dimension ≤ 1. The ℵ‐uniformity of a Tychonoff spaceX, which is generated by all open normal coverings ofXwith cardinality ≤ℵ, is complete iffXcan be embedded as a closed subspace in a Cartesian product

ISSN:0077-8923    

DOI:10.1111/j.1749-6632.1992.tb32246.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

It is assumed that X is an abstract set and ℒ is a lattice of subsets of X. The consequences of ℒ being regular, and of ℒ being regular together with other lattice properties such as prime complete or even Lindelöf, are discussed first. Next, the important problem of enlarging an ℒ‐filter or an ℒ‐ultrafilter with the countable intersection property is considered. It is much easier to express this in terms of zero–one‐valued finitely additive measures on the algebra generated by ℒ. Conditions for the preceding to hold in terms of topological spaces of measures associated with the lattice

ISSN:0077-8923    

DOI:10.1111/j.1749-6632.1992.tb32247.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

It is known that closed maps preserve θ‐refinability and subparacompactness. It is also known that perfect maps preserve weak θ‐refinability. Some results toward a perfect mapping theorem forB(D, ω0)‐refinability are given, as well as some results on sum theorems for this

ISSN:0077-8923    

DOI:10.1111/j.1749-6632.1992.tb32248.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

A. R. Bernstein introduced the concept ofp‐compactness (p∈ω*). Years later, W. W. Comfort defined a (pre)‐order ≤Con ω* byp ≤Cqiff everyq‐compact space isp‐compact. It is natural to consider the relation ≤GCon ω* given byp≤GCq iff everyq‐compact topological group isp‐compact. It is shown that ≤RK≤C, and ≤GCcoincide on the set of weakP‐points of ω* (≤RKdenotes the Rudin–Keisler order on ω*), and that ≤Cand ≤GChave several properties in common, but the question whether ≤C=≤GCstill remains unsolved. Some properties of freeM‐compact groups (M⊆α*) are also studied. In particular, it is shown that if α is a regular infinite cardinal andXis<α‐bounded, thenXis a closed subspace

ISSN:0077-8923    

DOI:10.1111/j.1749-6632.1992.tb32249.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY

摘要:

The main theorem characterizes the quasi‐perfect and perfect preimages ofT1‐spaces having a base of countable order. The preimages ofT1‐spaces having a base of countable order are connected with the preimages ofT1‐spaces having a primitive base under the same type of m

ISSN:0077-8923    

DOI:10.1111/j.1749-6632.1992.tb32250.x

出版商:Blackwell Publishing Ltd    

年代:1992

数据来源: WILEY