scholarly journals The space of contractive C0-semigroups is a Baire space

2022 ◽  
Vol 508 (1) ◽  
pp. 125881
Author(s):  
Raj Dahya
Keyword(s):  
Baire Space

The weak König lemma and uniform continuity

2008 ◽  
Vol 73 (3) ◽  
pp. 933-939 ◽  
Author(s):  
Josef Berger
Keyword(s):  
Continuous Function ◽  
Uniform Continuity ◽  
Baire Space ◽  
Cantor Space

AbstractWe prove constructively that the weak König lemma and quantifier-free number–number choice imply that every pointwise continuous function from Cantor space into Baire space has a modulus of uniform continuity.

scholarly journals Baire space and second category extensions

1981 ◽  
Vol 12 (2) ◽  
pp. 135-140 ◽  
Author(s):  
John W. Carlson
Keyword(s):  
Baire Space ◽  
Second Category

Completeness properties of the pseudocompact-open topology on C(X)

2008 ◽  
Vol 58 (3) ◽  
Author(s):  
S. Kundu ◽  
Pratibha Garg
Keyword(s):  
Function Space ◽  
Baire Space ◽  
Tychonoff Space ◽  
Complete Metrizability ◽  
Space Property

AbstractThis is a study of the completeness properties of the space C ps(X) of continuous real-valued functions on a Tychonoff space X, where the function space has the pseudocompact-open topology. The properties range from complete metrizability to the Baire space property.

FAILURES OF THE SILVER DICHOTOMY IN THE GENERALIZED BAIRE SPACE

2015 ◽  
Vol 80 (2) ◽  
pp. 661-670 ◽  
Author(s):  
SY-DAVID FRIEDMAN ◽  
VADIM KULIKOV
Keyword(s):  
Baire Space ◽  
Equivalence Relations ◽  
Borel Equivalence Relations

AbstractWe prove results that falsify Silver’s dichotomy for Borel equivalence relations on the generalized Baire space under the assumptionV=L.

scholarly journals The Borel structure of iterates of continuous functions

1989 ◽  
Vol 32 (3) ◽  
pp. 483-494 ◽  
Author(s):  
Paul D. Humke ◽  
M. Laczkovich
Keyword(s):  
Banach Space ◽  
Continuous Functions ◽  
Baire Space ◽  
Space Of Continuous Functions ◽  
Borel Structure ◽  
Image Position ◽  
Set Of Points ◽  
Positive Integers

Let C[0,1] be the Banach space of continuous functions defined on [0,1] and let C be the set of functions f∈C[0,1] mapping [0,1] into itself. If f∈C, fk will denote the kth iterate of f and we put Ck = {fk:f∈C;}. The set of increasing (≡ nondecreasing) and decreasing (≡ nonincreasing) functions in C will be denoted by ℐ and D, respectively. If a function f is defined on an interval I, we let C(f) denote the set of points at which f is locally constant, i.e.We let N denote the set of positive integers and NN denote the Baire space of sequences of positive integers.

scholarly journals On Almost Continuous Mappings and Baire Spaces

1978 ◽  
Vol 21 (2) ◽  
pp. 183-186 ◽  
Author(s):  
Shwu-Yeng T. Lin ◽  
You-Feng Lin
Keyword(s):  
Topological Space ◽  
Dense Subset ◽  
Baire Space ◽  
Real Numbers ◽  
Range Space ◽  
Continuous Mappings ◽  
Almost Continuous

AbstractIt is proved, in particular, that a topological space X is a Baire space if and only if every real valued function f: X →R is almost continuous on a dense subset of X. In fact, in the above characterization of a Baire space, the range space R of real numbers may be generalized to any second countable, Hausdorfï space that contains infinitely many points.

scholarly journals Note on limits of simply continuous and cliquish functions

1994 ◽  
Vol 17 (3) ◽  
pp. 447-450 ◽  
Author(s):  
Janina Ewert
Keyword(s):  
Metric Space ◽  
Continuous Functions ◽  
Baire Space ◽  
Baire Property ◽  
Baire Class ◽  
Class 1 ◽  
Pointwise Limit ◽  
Separable Metric Space

The main result of this paper is that any functionfdefined on a perfect Baire space(X,T)with values in a separable metric spaceYis cliquish (has the Baire property) iff it is a uniform (pointwise) limit of sequence{fn:n≥1}of simply continuous functions. This result is obtained by a change of a topology onXand showing that a functionf:(X,T)→Yis cliquish (has the Baire property) iff it is of the Baire class 1 (class 2) with respect to the new topology.

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