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Nonnormality or hereditary paracompactness of some spaces of real
AL %r U Lax y' d paracompactness of some s*%aces, of real functions Eric K. van ... EX., Nonnormality or hereditary paracompactness of some spaces of real ...
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The m-topology on Cm(X) revisited - ScienceDirect
... Nonnormality or hereditary paracompactness of some spaces of real functions, Topology Appl. 39 (1) (1991) 3–32] completing a characterization of when C m ...
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The m-topology on Cm(X) revisited - Bowling Green State University
verse of a theorem of van Douwen [E. van Douwen, Nonnormality or hereditary paracompactness of some spaces of real functions, Topology Appl. 39 (1) (1991)  ...
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LINDEL¨OF POWERS AND PRODUCTS OF FUNCTION SPACES
We denote by Cp(X) the space of all continuous real-valued functions .... Note that for some i ∈ ω, the projection πi(F) is uncountable, because F is ..... of which is Lindelöf and the other second-countable, whose product is nonnormal .... [Pr2] T. C. Przymusinski, Normality and paracompactness in finite and Cartesian ...
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NORMALITY AND PROPERTIES RELATED TO COMPACTNESS IN
pact ordinal space, then 2X is nonnormal. In this paper we give ... The paracompactness of. 2X is shown to ... In the last part of the paper some properties related to the countable compactness ... valued functions), there must be at least 22' continuous real valued functions on 2X. Thus we .... It is productive, closed hereditary,.
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Free full version - Auburn University
assumptions, of nonnormal collectionwise T. Moore spaces. 2 .... one would expect that if a QD-space has a certain base pro perty then ... verting hereditary covering properties or hereditary collec tionwise .... spaces with a-LCB's are metrizable iff they are paracompact. ... (c) an O-metric space if there is a function p mapping.
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Another generalization of the m-topology - Hikari
real valued continuous functions on a completely regular Hausdorff space X. ..... [ 3] E. van Douwen, Nonnormality or hereditary paracompactness of some.
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On α-normal and β-normal spaces
ately leads to generalizations of some important results on normal spaces. ... properties, such as metacompactness, strong paracompactness, countable para .... following spaces are not α-normal (the standard proofs of their non-normality ..... [19] Šcepin E.V., Real functions and spaces that are nearly normal, Siberian Math.
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F. Azarpanah, M. Paimann, A.R. Salehi Connectedness of some
Connectedness of some rings of quotients of C(X) with the m-topology ... [5] Fine N.J., Gillman L., Lambek J., Rings of quotients of rings of continuous functions, ... E.K., Nonnormality or hereditary paracompactness of some spaces of real func-.
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Spaces with bases satisfying certain order and intersection properties
strong quasi-uniform base (unlike the earlier properties) is not hereditary. [21]. ... Thus, for example, the Michael line, the discretization of the real line obtained by ... stronger result obtains in this case: every paracompact space with an ortho- base can ..... is quasi-metrizable if and only if, it admits a function satisfying (A) and.
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Sum theorems for topological spaces - MSP
belongs to some class Q of topological spaces. When can we ... we show that (Σ) also holds for point wise paracompact spaces. The main ... 1 is due to the nonnormality of X. And in fact, every normal space which is a ... Each of these classes is hereditary ..... L. Gillman and M. Jerison, Rings of continuous functions, 1960. 7.
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Linearly Ordered and Generalized Ordered Spaces - College of
May 6, 2002 ... genfrey line, and the Michael line (i.e., the usual space of real ... topological spaces have the open interval topology of some linear order (the or- ... is orderable; there is a continuous function f : 2X → X with f(T) ∈ T for each ... and Lutzer: a GO-space X is paracompact if and only if no closed subspace of.
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The space $\ omega^* $ and the reconstruction of normality
Jan 20, 2015 ... space X if Y is homeomorphic to X < 1xl for some x in X. The deck ... X. For example, if Y is a card of the real line, then Y is homeomorphic ... Reconstruction, ω*, normality, paracompactness, F -space, Stone- ... normal space containing a Gδ-point, since normality is hereditary ... function f is called a zero-set.
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metrizability of topological spaces - Project Euclid
collectionwise normal spaces are always TΊ and paracompact spaces are always Hausdorff. ... distinct points p and q in X, there is some G in ^ such that p e G,. qίG . .... Let (X, J7~) be a topological space, let g be a function from. N x X into ...... with the topology described in [28]) is a completely regular nonnormal screenable ...
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Continuing horrors of topology without choice
Metrization Theorem is entirely effective, whilst recalling that some choice is ... R is paracompact and o1 may be paracompact but never metrizable. An ... compact space on which every continuous real-valued function is constant. ..... [21] E.K. van Douwen, Horrors of topology without AC: a nonnormal orderable space, Proc .
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OPEN PROBLEMS IN VAN DOUWEN'S PAPERS From the preface
(6) Simultaneous extension of continuous functions. (7) Box products .... nality at most c is a quasi-perfect image of some locally compact space. Open. 24.
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Disconnectedness Properties in Hyperspaces, Spaces of Remote
Mar 1, 2013 ... 3.2 Some spaces such that K(X) = F(X) . ..... Lemma 0.1 If κ is a regular cardinal, then there is a function φ : κ → κ such that {β<κ ..... A space X is paracompact if X is Hausdorff and every open cover of X has ... R set of real numbers ... The chapter about hereditary disconnectedness is the most complex in this.
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A Study of Non-Euclidean s-Topology
May 28, 2012 ... the fine topology is separable, Hausdorff, nonnormal, nonlocally ... subspace topologies on certain subsets of Minkowski space with s-topology. ..... of all continuous real-valued functions on Ms is at most equal to 2 ... Then since second countability is a hereditary property, it .... Then Ms is not paracompact.
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Applications of Reflection to Topology - TSpace - University of Toronto
2.2 Preserving hereditary normality for spaces of small pointwise type ... . ... 3.5 Some remarks on the large cardinal versus the elementary submodel ... spaces. A simple example is the real line: if 2'0 = N1 then there is a family of wl first .... the fact that j(K) > a, the fact that forcing with Cohen reals preserves non-normality.
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Products of Lindelöf T2-spaces are Lindelöf — in some models of ZF
Arbitrary products and countable sums of compact T1-spaces are Lindelöf. iff AC holds. ... the set R of real numbers the product ∏ Xn is not empty. 4. CMC, the ... ( b) all Lindelöf T3-spaces are paracompact and realcompact. .... In ZF the Lindelöf -property is closed-hereditary. Thus in ..... choice-function for the sequence (Xn).
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