Displaying similar documents to “On the sequential order continuity of the C ( K ) -space.”

Algebraic properties of rings of continuous functions

M. Mulero (1996)

Fundamenta Mathematicae

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This paper is devoted to the study of algebraic properties of rings of continuous functions. Our aim is to show that these rings, even if they are highly non-noetherian, have properties quite similar to the elementary properties of noetherian rings: we give going-up and going-down theorems, a characterization of z-ideals and of primary ideals having as radical a maximal ideal and a flatness criterion which is entirely analogous to the one for modules over principal ideal domains. ...

Examples of sequential topological groups under the continuum hypothesis

Alexander Shibakov (1996)

Fundamenta Mathematicae

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Using CH we construct examples of sequential topological groups: 1. a pair of countable Fréchet topological groups whose product is sequential but is not Fréchet, 2. a countable Fréchet and α 1 topological group which contains no copy of the rationals.

On finite sum theorems for transfinite inductive dimensions

Vitalij Chatyrko (1999)

Fundamenta Mathematicae

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We discuss the exactness of estimates in the finite sum theorems for transfinite inductive dimensions trind and trInd. The technique obtained gives an opportunity to repeat and sometimes strengthen some well known results about compacta with trind ≠ trInd. In particular we improve an estimate of the small transfinite inductive dimension of Smirnov’s compacta S α , α < ω 1 , given by Luxemburg [Lu2].

On spirals and fixed point property

Roman Mańka (1994)

Fundamenta Mathematicae

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We study the famous examples of G. S. Young [7] and R. H. Bing [2]. We generalize and simplify a little their constructions. First we introduce Young spirals which play a basic role in all considerations. We give a construction of a Young spiral which does not have the fixed point property (see Section 5) . Then, using Young spirals, we define two classes of uniquely arcwise connected curves, called Young spaces and Bing spaces. These classes are analogous to the examples mentioned above....

Note on some greatest common divisor matrices

Peter Lindqvist, Kristian Seip (1998)

Acta Arithmetica

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Some quadratic forms related to "greatest common divisor matrices" are represented in terms of L²-norms of rather simple functions. Our formula is especially useful when the size of the matrix grows, and we will study the asymptotic behaviour of the smallest and largest eigenvalues. Indeed, a sharp bound in terms of the zeta function is obtained. Our leading example is a hybrid between Hilbert's matrix and Smith's matrix.

Strong meager properties for filters

Claude Laflamme (1995)

Fundamenta Mathematicae

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We analyze several “strong meager” properties for filters on the natural numbers between the classical Baire property and a filter being F σ . Two such properties have been studied by Talagrand and a few more combinatorial ones are investigated. In particular, we define the notion of a P⁺-filter, a generalization of the traditional concept of P-filter, and prove the existence of a non-meager P⁺-filter. Our motivation lies in understanding the structure of filters generated by complements...

K-theory, flat bundles and the Borel classes

Bjørn Jahren (1999)

Fundamenta Mathematicae

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Using Hausmann and Vogel's homology sphere bundle interpretation of algebraic K-theory, we construct K-theory invariants by a theory of characteristic classes for flat bundles. It is shown that the Borel classes are detected this way, as well as the rational K-theory of integer group rings of finite groups.

Interpreting reflexive theories in finitely many axioms

V. Shavrukov (1997)

Fundamenta Mathematicae

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For finitely axiomatized sequential theories F and reflexive theories R, we give a characterization of the relation ’F interprets R’ in terms of provability of restricted consistency statements on cuts. This characterization is used in a proof that the set of ∏ 1 (as well as ∑ 1 ) sentences π such that GB interprets ZF+π is Σ 3 0 -complete.

ℳ-rank and meager types

Ludomir Newelski (1995)

Fundamenta Mathematicae

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Assume T is superstable and small. Using the multiplicity rank ℳ we find locally modular types in the same manner as U-rank considerations yield regular types. We define local versions of ℳ-rank, which also yield meager types.