scholarly journals Mappings and decompositions of continuity on almost Lindelöf spaces

2006 ◽  
Vol 2006 ◽  
pp. 1-7 ◽  
Author(s):  
A. J. Fawakhreh ◽  
A. Kiliçman
Keyword(s):  
Topological Space ◽  
Open Cover ◽  
Countable Subset

A topological spaceXis said to be almost Lindelöf if for every open cover{Uα:α∈Δ}ofXthere exists a countable subset{αn:n∈ℕ}⊆Δsuch thatX=∪n∈ℕCl(Uαn). In this paper we study the effect of mappings and some decompositions of continuity on almost Lindelöf spaces. The main result is that a image of an almost Lindelöf space is almost Lindelöf.

scholarly journals Remarks on neighborhood star-Lindelöf spaces II

Filomat ◽  
2013 ◽  
Vol 27 (5) ◽  
pp. 875-880
Author(s):  
Yan-Kui Song
Keyword(s):  
Open Cover ◽  
Countable Subset ◽  
Topological Properties ◽  
Pseudocompact Spaces ◽  
The Relationship

A space X is said to be neighborhood star-Lindel?f if for every open cover U of X there exists a countable subset A of X such that for every open O?A, X=St(O,U). In this paper, we continue to investigate the relationship between neighborhood star-Lindel?f spaces and related spaces, and study topological properties of neighborhood star-Lindel?f spaces in the classes of normal and pseudocompact spaces. .

scholarly journals Paracompactness with respect to an ideal

1997 ◽  
Vol 20 (3) ◽  
pp. 433-442 ◽  
Author(s):  
T. R. Hamlett ◽  
David Rose ◽  
Dragan Janković
Keyword(s):  
Topological Space ◽  
Finite Union ◽  
Open Cover ◽  
Locally Finite ◽  
Open Set ◽  
Special Cases ◽  
Paracompact Spaces

An ideal on a setXis a nonempty collection of subsets ofXclosed under the operations of subset and finite union. Given a topological spaceXand an idealℐof subsets ofX,Xis defined to beℐ-paracompact if every open cover of the space admits a locally finite open refinement which is a cover for all ofXexcept for a set inℐ. Basic results are investigated, particularly with regard to theℐ- paracompactness of two associated topologies generated by sets of the formU−IwhereUis open andI∈ℐand⋃{U|Uis open andU−A∈ℐ, for some open setA}. Preservation ofℐ-paracompactness by functions, subsets, and products is investigated. Important special cases ofℐ-paracompact spaces are the usual paracompact spaces and the almost paracompact spaces of Singal and Arya [“On m-paracompact spaces”, Math. Ann., 181 (1969), 119-133].

scholarly journals A generalization of a theorem of Aquaro

1973 ◽  
Vol 9 (1) ◽  
pp. 105-108 ◽  
Author(s):  
C.E. Aull
Keyword(s):  
Topological Space ◽  
Compact Space ◽  
Continuum Hypothesis ◽  
Open Cover ◽  
Moore Space ◽  
Countably Compact Space ◽  
Classic Result ◽  
Countably Compact ◽  
The Continuum

In this paper we introduce the concept of a δθ-cover to generalize Aquaro's Theorem that every point countable open cover of a topological space such that every discrete closed family of sets is countable has a countable subcover. A δθ-cover of a space X is defined to be a family of open sets where each Vn covers X and for x є X there exists n such that Vn is of countable order at x. We replace point countable open cover by a δθ-cover in Aquaro's Theorem and also generalize the result of Worrell and Wicke that a θ-refinable countably compact space is compact and Jones′ result that ℵ1-compact Moore space is Lindelöf which was used to prove his classic result that a normal separable Moore space is metrizable, using the continuum hypothesis.

scholarly journals On paracompact regular spaces

1961 ◽  
Vol 2 (2) ◽  
pp. 147-150
Author(s):  
Shuen Yuan
Keyword(s):  
Topological Space ◽  
Finite Number ◽  
Recent Result ◽  
Open Cover ◽  
Regular Space ◽  
Locally Finite ◽  
Normality Condition ◽  
Discrete Family

A topological space is paracompact if and only if each open cover of the space has an open locally finite refinement. It is well-known that an unusual normality condition is satisfied by each paracompact regular space X [p. 158, 5]: Let α be a locally finite (discrete) family of subsets of X, then there is a neighborhood V of the diagonal Δ(X) (in X × X), such that V[x] intersects at most a finite number of members (respectively at most one member) of {V[A]: A ∈ α} for each x ∈ X. In this not we will show that a variant of this condition actually characterizes paracompactness. Among other results, an improvement to a recent result of H. H.Corson [2] is given so as to accord with a conjecture of J. L. Kelley [p. 208, 5] more prettily, and we connect paracompactness to metacompactness [1]

Even Covering Properties and Somewhat Normal Spaces

1986 ◽  
Vol 29 (2) ◽  
pp. 154-159
Author(s):  
Hans-Peter Künzi ◽  
Peter Fletcher
Keyword(s):  
Topological Space ◽  
Open Cover ◽  
Normal Space ◽  
Completely Regular ◽  
Covering Properties ◽  
Normal Cover

AbstractA topological space X is said to be somewhat normal provided that for each open cover is a normal cover of X. We show that a completely regular somewhat normal space need not be normal, thereby answering a question of W. M. Fleischman. We note that a collectionwise normal somewhat normal space need not be almost 2-fully normal, as had previously been asserted, and that neither the perfect image nor the perfect preimage of a somewhat normal space has to be somewhat normal.

scholarly journals Generalized products of weakly m — n compact spaces, I

1982 ◽  
Vol 33 (2) ◽  
pp. 143-151 ◽  
Author(s):  
U. N. B. Dissanayake
Keyword(s):  
Topological Space ◽  
Sufficient Conditions ◽  
Open Cover ◽  
Compact Spaces

AbstractA topological space X is said to be weakly-Lindelöf if and only if every open cover of X has a countable sub-family with dense union. We know that products of two Lindelöf spaces need not be weakly-Lindelöf. In this paper we obtain non-trivial sufficient conditions on small sub-products to ensure the producitivity of the property weakly-Lindelöf with respect to arbitrary products.

Some remarks on almost star countable spaces

2015 ◽  
Vol 52 (1) ◽  
pp. 12-20
Author(s):  
Yan-Kui Song
Keyword(s):  
Open Cover ◽  
Countable Subset ◽  
Topological Properties ◽  
Star Countable

A space X is almost star countable (weakly star countable) if for each open cover U of X there exists a countable subset F of X such that \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\bigcup {_{x \in F}\overline {St\left( {x,U} \right)} } = X$ \end{document} (respectively, \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\overline {\bigcup {_{x \in F}} St\left( {x,U} \right)} = X$ \end{document}. In this paper, we investigate the relationships among star countable spaces, almost star countable spaces and weakly star countable spaces, and also study topological properties of almost star countable spaces.

Transitivity and Ortho-Bases

1981 ◽  
Vol 33 (6) ◽  
pp. 1439-1447 ◽  
Author(s):  
Jacob Kofner
Keyword(s):  
Topological Space ◽  
Open Cover ◽  
Local Base

Throughout this paper “space” means “T1 topological space.“1. The concept of an ortho-base was introduced by W. F. Lindgren and P. J. Nyikos.Definition 1. A base of a space X is called an ortho-base provided that for each subcollection either is open or is a local base of a point x ∊ X [17].Ortho-bases are related to interior-preserving collections which have been known for some time.Definition 2. A collection of open sets of a space X is called interior-preserving provided that the intersection of any subcollection is open. A space X is called orthocompact provided that each open cover has an open interior-preserving refinement.It was proved in [17], in particular, that each space with an ortho-base is orthocompact, and each orthocompact developable space (which is the same as a non-archimedean quasi-metrizable developable space [4]) has an ortho-base.

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