9. Baire Category Theorem

2016 ◽  
pp. 126-136
Keyword(s):  
Baire Category ◽  
Baire Category Theorem ◽  
Category Theorem

scholarly journals The closed graph theorem without category

1987 ◽  
Vol 36 (2) ◽  
pp. 283-287 ◽  
Author(s):  
Charles Swartz
Keyword(s):  
Baire Category ◽  
Baire Category Theorem ◽  
Normed Spaces ◽  
Closed Graph ◽  
Graph Theorem ◽  
Closed Graph Theorem ◽  
Category Theorem

We show that a diagonal theorem of P. Antosik can be used to give a proof of the Closed Graph Theorem for normed spaces which does not depend upon the Baire Category Theorem.

The Baire category theorem in weak subsystems of second-order arithmetic

1993 ◽  
Vol 58 (2) ◽  
pp. 557-578 ◽  
Author(s):  
Douglas K. Brown ◽  
Stephen G. Simpson
Keyword(s):  
Functional Analysis ◽  
Model Theory ◽  
Baire Category ◽  
Second Order ◽  
Base System ◽  
Baire Category Theorem ◽  
Second Order Arithmetic ◽  
Category Theorem ◽  
Order Arithmetic

AbstractWorking within weak subsystems of second-order arithmetic Z2 we consider two versions of the Baire Category theorem which are not equivalent over the base system RCA0. We show that one version (B.C.T.I) is provable in RCA0 while the second version (B.C.T.II) requires a stronger system. We introduce two new subsystems of Z2, which we call and , and , show that suffices to prove B.C.T.II. Some model theory of and its importance in view of Hilbert's program is discussed, as well as applications of our results to functional analysis.

scholarly journals Some remarks on fuzzy k-pseudometric spaces

Filomat ◽  
2018 ◽  
Vol 32 (10) ◽  
pp. 3567-3580 ◽  
Author(s):  
Alexander Sostak
Keyword(s):  
Metric Spaces ◽  
Baire Category ◽  
Important Class ◽  
Baire Category Theorem ◽  
Category Theorem ◽  
Type Spaces ◽  
Fixed Constant

An important class of spaces was introduced by I.A. Bakhtin (under the name ?metric-type?) and independently rediscovered by S. Czerwik (under the name ?b-metric?). Metric-type spaces generalize ?classic? metric spaces by replacing the triangularity axiom with a more general axiom d(x,z)? k? (d(x,y)+ d(y,z)) for all x,y,z ? X where k ? 1 is a fixed constant. Recently R. Saadadi has introduced the fuzzy version of ?metric-type? spaces. In this paper we consider topological and sequential properties of such spaces, illustrate them by several examples and prove a certain version of the Baire Category Theorem.

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