On countable paracompactness and normality

P. Zenor

doi:10.14708/cm.v13i1.5653

Sum Theorems for Countably Paracompact Spaces

Canadian Journal of Mathematics ◽

10.4153/cjm-1973-072-5 ◽

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].

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Product Maps and Countable Paracompactness

Canadian Journal of Mathematics ◽

10.4153/cjm-1972-128-7 ◽

1972 ◽

Vol 24 (6) ◽

pp. 1187-1190 ◽

Cited By ~ 1

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.

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Countable Paracompactness and Souslin's Problem

Canadian Journal of Mathematics ◽

10.4153/cjm-1955-058-8 ◽

1955 ◽

Vol 7 ◽

pp. 543-547 ◽

Cited By ~ 22

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).

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