Weak normality properties and countable paracompactness

2020 ◽  
Vol 275 ◽  
pp. 107016
Author(s):  
A.V. Bogomolov
Keyword(s):  
Weak Normality ◽  
Countable Paracompactness

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].

Product Maps and Countable Paracompactness

1972 ◽  
Vol 24 (6) ◽  
pp. 1187-1190 ◽  
Author(s):  
Harold W. Martin
Keyword(s):  
Usual Topology ◽  
Continuous Surjection ◽  
Product Maps ◽  
Countable Paracompactness

In all that follows, we let S denote the space {0, 1, 1/2, … , 1/n, …} with the relative usual topology and i : S → S denote the identity map on S. In this note, by a map or mapping we always mean a continuous surjection. A map f : X → Y is said to be hereditarily quotient if y ∊ int f(V) whenever V is open in X and f-1(y) ⊂ V. E. Michael has defined a map f : X → Y to be bi-quotient if whenever is a collection of open sets in X which covers f-1(y), there exists finitely many f(V), with V ∊ , which cover some neighbourhood of y.

Countable Paracompactness and Souslin's Problem

1955 ◽  
Vol 7 ◽  
pp. 543-547 ◽  
Author(s):  
Mary Ellen Rudin
Keyword(s):  
Ordered Space ◽  
Countable Paracompactness

1. Introduction. A linearly ordered space S in which neighborhoods are segments is called a Souslin space if(i) S is not separable, but(ii) every collection of disjoint segments of S is countable.Whether a Souslin space exists is not known; this is the problem referred to in the title and was proposed by Souslin in (2).

Countable paracompactness and normal functors

2015 ◽  
Vol 98 (5-6) ◽  
pp. 857-859
Author(s):  
A. P. Kombarov
Keyword(s):  
Countable Paracompactness
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