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

2022 ◽  
Vol 508 (1) ◽  
pp. 125881
Raj Dahya
2008 ◽  
Vol 73 (3) ◽  
pp. 933-939 ◽  
Josef Berger

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.

1981 ◽  
Vol 12 (2) ◽  
pp. 135-140 ◽  
John W. Carlson

2008 ◽  
Vol 58 (3) ◽  
S. Kundu ◽  
Pratibha Garg

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.

2015 ◽  
Vol 80 (2) ◽  
pp. 661-670 ◽  

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

1989 ◽  
Vol 32 (3) ◽  
pp. 483-494 ◽  
Paul D. Humke ◽  
M. Laczkovich

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.

1978 ◽  
Vol 21 (2) ◽  
pp. 183-186 ◽  
Shwu-Yeng T. Lin ◽  
You-Feng Lin

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.

1994 ◽  
Vol 17 (3) ◽  
pp. 447-450 ◽  
Janina Ewert

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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