scholarly journals Compact spaces, elementary submodels, and the countable chain condition

2006 ◽  
Vol 144 (1-3) ◽  
pp. 107-116 ◽  
Author(s):  
Lúcia R. Junqueira ◽  
Paul Larson ◽  
Franklin D. Tall
Keyword(s):  
Chain Condition ◽  
Compact Spaces ◽  
Elementary Submodels ◽  
Countable Chain Condition ◽  
Countable Chain

scholarly journals Lebesgue Measurability of Separately Continuous Functions and Separability

2007 ◽  
Vol 2007 ◽  
pp. 1-4
Author(s):  
V. V. Mykhaylyuk
Keyword(s):  
Topological Space ◽  
Chain Condition ◽  
Continuous Functions ◽  
Negative Answer ◽  
Regular Space ◽  
Property A ◽  
Completely Regular ◽  
Open Set ◽  
Countable Chain Condition ◽  
Countable Chain

A connection between the separability and the countable chain condition of spaces withL-property (a topological spaceXhasL-property if for every topological spaceY, separately continuous functionf:X×Y→ℝand open setI⊆ℝ,the setf−1(I)is anFσ-set) is studied. We show that every completely regular Baire space with theL-property and the countable chain condition is separable and constructs a nonseparable completely regular space with theL-property and the countable chain condition. This gives a negative answer to a question of M. Burke.

scholarly journals A characterization of the existence of a Souslin line

1982 ◽  
Vol 25 (3) ◽  
pp. 425-431
Author(s):  
Nobuyuki Kemoto
Keyword(s):  
Disjoint Union ◽  
Chain Condition ◽  
First Category ◽  
Countable Chain Condition ◽  
Isolated Points ◽  
Countable Chain

The main purpose of this paper is to show that there exists a Souslin line if and only if there exists a countable chain condition space which is not weak-separable but has a generic π-base. If I is the closure of the isolated points in a space X, then X is said to be weak-separable if a first category set is dense in X – I. A π-base is said to be generic if, whenever a member of is included in the disjoint union of members of it is included in one of them.

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