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Algebraic properties of rings of continuous functions

M. Mulero (1996)

Fundamenta Mathematicae

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.

Algebras and spaces of dense constancies

Angelo Bella, Jorge Martinez, Scott D. Woodward (2001)

Czechoslovak Mathematical Journal

A DC-space (or space of dense constancies) is a Tychonoff space X such that for each f ∈ C ( X ) there is a family of open sets { U i i ∈ I } , the union of which is dense in X , such that f , restricted to each U i , is constant. A number of characterizations of DC-spaces are given, which lead to an algebraic generalization of the concept, which, in turn, permits analysis of DC-spaces in the language of archimedean f -algebras. One is led naturally to the notion of an almost DC-space (in which the densely constant functions...

Algebras of Borel measurable functions

Michał Morayne (1992)

Fundamenta Mathematicae

We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.

All CAT(0) boundaries of a group of the form H × K are CE equivalent

Christopher Mooney (2009)

Fundamenta Mathematicae

M. Bestvina has shown that for any given torsion-free CAT(0) group G, all of its boundaries are shape equivalent. He then posed the question of whether they satisfy the stronger condition of being cell-like equivalent. In this article we prove that the answer is "Yes" in the situation where the group in question splits as a direct product with infinite factors. We accomplish this by proving an interesting theorem in shape theory.

Almost continuity vs closure continuity

B. A. Saleemi, Naseer Shahzad, M. A. Alghamdi (2001)

Archivum Mathematicum

We provide an answer to a question: under what conditions almost continuity in the sense of Husain implies closure continuity?

Almost g ˜ α -closed functions and separation axioms

O. Ravi, S. Ganesan, R. Latha (2012)

Mathematica Bohemica

We introduce a new class of functions called almost g ˜ α -closed and use the functions to improve several preservation theorems of normality and regularity and also their generalizations. The main result of the paper is that normality and weak normality are preserved under almost g ˜ α -closed continuous surjections.

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