scholarly journals A class of countably paracompact spaces

1970 ◽  
Vol 24 (2) ◽  
pp. 258-258 ◽  
Author(s):  
Phillip Zenor
Keyword(s):  
Countably Paracompact ◽  
Paracompact Spaces

Sum Theorems for Countably Paracompact Spaces

1973 ◽  
Vol 25 (4) ◽  
pp. 706-711
Author(s):  
Henry Potoczny
Keyword(s):  
Open Cover ◽  
Equivalent Formulation ◽  
Countably Paracompact ◽  
Definition Of ◽  
Paracompact Spaces ◽  
Countable Paracompactness

In this paper, we extend the class of spaces to which the Σ and β theorems of Hodel apply, as well as the sum and subset theorems of [2]. Instead of the open cover definition of countable paracompactness, we utilize an equivalent formulation of countable paracompactness, due to Ishikawa [3].

scholarly journals Characterizations of Strongly Paracompact Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-5
Author(s):  
Xin Zhang
Keyword(s):  
Open Cover ◽  
Normal Space ◽  
Compact Spaces ◽  
Countably Paracompact ◽  
Star Countable ◽  
Perfectly Normal Space ◽  
Paracompact Spaces ◽  
Perfectly Normal

Characterizations of strongly compact spaces are given based on the existence of a star-countable open refinement for every increasing open cover. It is proved that a countably paracompact normal space (a perfectly normal space or a monotonically normal space) is strongly paracompact if and only if every increasing open cover of the space has a star-countable open refinement. Moreover, it is shown that a space is linearlyDprovided that every increasing open cover of the space has a point-countable open refinement.

On Countably Paracompact Spaces

1951 ◽  
Vol 3 ◽  
pp. 219-224 ◽  
Author(s):  
C. H. Dowker
Keyword(s):  
Topological Space ◽  
Finite Number ◽  
Finite Collection ◽  
Countable Collection ◽  
Locally Finite ◽  
Open Set ◽  
Countably Paracompact ◽  
Paracompact Spaces ◽  
Countable Covering

Let X be a topological space, that is, a space with open sets such that the union of any collection of open sets is open and the intersection of any finite number of open sets is open. A covering of X is a collection of open sets whose union is X. The covering is called countable if it consists of a countable collection of open sets or finite if it consists of a finite collection of open sets ; it is called locally finite if every point of X is contained in some open set which meets only a finite number of sets of the covering. A covering is called a refinement of a covering U if every open set of X is contained in some open set of . The space X is called countably paracompact if every countable covering has a locally finite refinement.

A note on boundedly countably paracompact spaces

Mathematika ◽  
1971 ◽  
Vol 18 (2) ◽  
pp. 168-171
Author(s):  
P. Fletcher ◽  
R. A. McCoy ◽  
R. Slover
Keyword(s):  
Countably Paracompact ◽  
Paracompact Spaces
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