共查询到20条相似文献,搜索用时 109 毫秒
1.
Harald Brandenburg 《Topology and its Applications》1983,15(3):223-229
A second countable developable T1-space 1 is defined which has the following properties: (1) 1 is an absolute extensor for the class of perfect spaces. (2) 1?0 is a universal space for second countable developable T1-spaces. 相似文献
2.
R.Grant Woods 《Topology and its Applications》1985,21(3):287-295
Let be a closed-hereditary topological property preserved by products. Call a space -regular if it is homeomorphic to a subspace of a product of spaces with . Suppose that each -regular space possesses a -regular compactification. It is well-known that each -regular space X is densely embedded in a unique space γscPX with such that if f: X → Y is continuous and Y has , then f extends continuously to γscPX. Call -pseudocompact if γscPX is compact.Associated with is another topological property #, possessing all the properties hypothesized for above, defined as follows: a -regular space X has # if each -pseudocompact closed subspace of X is compact. It is known that the -pseudocompact spaces coincide with the #-pseudocompact spaces, and that # is the largest closed-hereditary, productive property for which this is the case. In this paper we prove that if is not the property of being compact and -regular, then # is not simply generated; in other words, there does not exist a space E such that the spaces with # are precisely those spaces homeomorphic to closed subspaces of powers of E. 相似文献
3.
H.H. Hung 《Topology and its Applications》1982,14(2):163-165
We propose a generalization of Heath's theorem that semi-metric spaces with point-countable bases are developable: A semi-metrizable space X is developabale if (and only if) there is on it a σ-discrete family of closed sets, interior-preserving over each member C of which is a countable family {n(C): n ∈ N} of collections of open sets such that if U is a neighbourhood of ξ∈X, then there are such a Γ∈ and such a v∈ N that ξ ? Γ and ξ∈ int ∩ (D: ξ: D∈v(Γ))?U. 相似文献
4.
A space X is said to satisfy condition (C) if for every Y?X with |Y|=ω1, any family of open subsets of Y with ||=ω1 has a countable network. It is easy to see that if X satisfies condition (C), then its Pixley-Roy hyperspace [X] is CCC. We show that under MAω1 condition (C) is also necessary for [X] to be CCC, but under CH it is not. 相似文献
5.
Let X be a set. A collection of subsets of X has subinfinite rank if whenever ? , ∩≠ø, and is infinite, then there are two distinct elements of , one of which is a subset of the other. Theorem. AT1space with a base of subinfinite rank is hereditarily metacompact. 相似文献
6.
S. Purisch 《Topology and its Applications》1983,16(3):273-277
Let X be a nonarchimedean space and C be the union of all compact open subsets of X. The following conditions are listed in increasing order of generality. (Conditions 2 and 3 are equivalent.) 1. X is perfect; 2. C is an Fσ in X; 3. C? is metrizable; 4. X is orderable. It is also shown that X is orderable if is scattered or X is a GO space with countably many pseudogaps. An example is given of a non-orderable, totally disconnected, GO space with just one pseudogap. 相似文献
7.
Siegfried Graf 《Topology and its Applications》1981,12(3):247-256
The complete Boolean homomorphisms from the category algebra (X) of a complete matrix space X to the category algebra (Y) of a Baire topological space Y are characterized as those σ-homomorphisms which are induced by continuous maps from dense G8-subsets of Y into X. This result is used to deduce a series of related results in topology and measure theory (some of which are well-known). Finally a similar result for the complete Boolean homomorphisms from the category algebra (X) of a compact Hausdorff space X tothe category algebra (Y) of a Baire topological space Y is proved. 相似文献
8.
R.A. McCoy 《Topology and its Applications》1980,11(2):189-197
A study is made of the natural function which maps each point x of a space X to the evaluation function ex:Yx→Y defined by . A consequence of the results is that βX and υX can both be considered as subspaces of spaces of continous functions from appropriate domain spaces into I or R, respectively. 相似文献
9.
Petr Holický 《Topology and its Applications》2010,157(12):1926-275
We show that a metrizable space Y is completely metrizable if there is a continuous surjection f:X→Y such that the images of open (clopen) subsets of the (0-dimensional paracompact) ?ech-complete space X are resolvable subsets of Y (in particular, e.g., the elements of the smallest algebra generated by open sets in Y). 相似文献
10.
A completely regular space X is called nearly pseudocompact if υX?X is dense in βX?X, where βX is the Stone-?ech compactification of X and υX is its Hewitt realcompactification. After characterizing nearly pseudocompact spaces in a variety of ways, we show that X is nearly pseudocompact if it has a dense locally compact pseudocompact subspace, or if no point of X has a closed realcompact neighborhood. Moreover, every nearly pseudocompact space X is the union of two regular closed subsets X1, X2 such that Int X1 is locally compact, no points of X2 has a closed realcompact neighborhood, and . It follows that a product of two nearly pseudocompact spaces, one of which is locally compact, is also nearly pseudocompact. 相似文献
11.
Fons van Engelen 《Topology and its Applications》1984,17(3):275-285
Let X be separable, completely metrizable, and dense in itself. We show that if X admits a triple (D1, D2, h) of two countable dense subsets D1 and D2 and a homeomorphism h: X?D1 → X?D2, satisfying some special properties, then there is a rigid subspace A of X such that A is homeomorphic to X?A = h[A]; for , such atriple is shown to exist. 相似文献
12.
The following result, and a closely related one, is proved: If u:X → Y is an open, perfect surjection, with X metrizable and with dim X = 0 or dim Y = 0, then there exists a perfect surjection such that u ° h = πY (where S in the Cantor set and is the projection). If moreover, u-1(y) is homeomorphic to S for all y?Y, then h can be chosen to be a homeomorphism. 相似文献
13.
Alessandro Berarducci Dikran Dikranjan Jan Pelant 《Topology and its Applications》2009,156(7):1422-1437
A metric space X is straight if for each finite cover of X by closed sets, and for each real valued function f on X, if f is uniformly continuous on each set of the cover, then f is uniformly continuous on the whole of X. A locally connected space is straight iff it is uniformly locally connected (ULC). It is easily seen that ULC spaces are stable under finite products. On the other hand the product of two straight spaces is not necessarily straight. We prove that the product X×Y of two metric spaces is straight if and only if both X and Y are straight and one of the following conditions holds:
- (a)
- both X and Y are precompact;
- (b)
- both X and Y are locally connected;
- (c)
- one of the spaces is both precompact and locally connected.
14.
Two square matrices A and B over a ring R are semisimilar, written AB, if YAX=B and XBY=A for some (possibly rectangular) matrices X, Y over R. We show that if A and B have the same dimension, and if the ring is a division ring , then AB if and only if A2 is similar to B2 and rank(Ak)=rank(Bk), k=1,2,… 相似文献
15.
Haruto Ohta 《Topology and its Applications》1984,17(3):265-274
In response to questions of Ginsburg [9, 10], we prove that if cf(c)>ω1, then there exists an open-closed, continuous map f from a normal, realcompact space X onto a space Y which is not realcompact. By his result the hyperspace 2x of closed subsets of X is then not realcompact, and the extension μf(vf) of f to the topological completion (the Hewitt realcompactification) of X is not onto. The latter fact solves problems raised by Morita [16] and by Isiwata [12] both negatively. We also consider the problem whether or not the hyperspace of a hereditarily Lindelöf space is hereditarily realcompact. 相似文献
16.
M.G. Tkačenko 《Topology and its Applications》1983,15(1):93-98
We consider the question: when is a dense subset of a space XC-embedded in X? We introduce the notion of o-tightness and prove that if each finite subproduct of a product X = Πα?AXα has a countable o-tightness and Y is a subset of X such that πB(Y) = Πα?BXα for every countable B ? A, then Y is C-embedded in X. This result generalizes some of Noble and Ulmer's results on C-embedding. 相似文献
17.
A family {Mα|α?A} is a shrinking of a cover {Oα|α?A} of a topological space if {Mα|α?A} also covers and Mα?Oα for all α?A.?++ implies that there is a normal space such that every increasing open cover of it has a clopen shrinking but there is an open cover having no closed shrinking.? implies that there is a P-space (i.e. a space having a normal product with every metric space), which has an increasing open cover having no closed shrinking. This space is used in [17] to show that any space which has a normal product with every P-space is metrizable. 相似文献
18.
Laurence Boxer 《Topology and its Applications》1980,11(1):17-29
Let X be a finite-dimensional compactum. Let (X) and (X) be the spaces of retractions and non-deformation retractions of X, respectively, with the compact-open (=sup-metric) topology. Let 2Xh be the space of non-empty compact ANR subsets of X with topology induced by the homotopy metric. Let RXh be the subspace of 2Xh consisting of the ANR's in X that are retracts of X.We show that (Sm) is simply-connected for m > 1. We show that if X is an ANR and A0?RXh, then limi→∞Ai=A0 in 2Xh if and only if for every retraction r0 of X onto A0 there are, for almost all i, retractions ri of X onto Ai such that limi→∞ri=ro in (X). We show that if X is an ANR, then the local connectedness of (X) implies that of RXh. We prove that (M) is locally connected if M is a closed surface. We give examples to show how some of our results weaken when X is not assumed to be an ANR. 相似文献
19.
Let X,Y be sets with quasiproximities X? and Y? (where A?B is interpreted as “B is a neighborhood of A”). Let f,g:X→Y be a pair of functions such that whenever CY?D, then f−1[C]X?g−1[D]. We show that there is then a function h:X→Y such that whenever CY?D, then f−1[C]X?h−1[D], h−1[C]X?h−1[D] and h−1[C]X?g−1[D]. Since any function h that satisfies h−1[C]X?h−1[D] whenever CY?D, is continuous, many classical “sandwich” or “insertion” theorems are corollaries of this result. The paper is written to emphasize the strong similarities between several concepts
- •
- the posets with auxiliary relations studied in domain theory;
- •
- quasiproximities and their simplification, Urysohn relations; and
- •
- the axioms assumed by Katětov and by Lane to originally show some of these results.
20.
E. Michael 《Topology and its Applications》2011,158(13):1526-1528
Principal result: Suppose Y is metrizable. Then: (a) if X is metrizable and A⊂X is closed, then every continuous g:A→Y extends to an l.s.c. ψ:X→K(Y); (b) Y satisfies (a) for all paracompact X if and only if Y is completely metrizable. 相似文献