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Network character and tightness of the compact-open topology

Richard N. Ball, Anthony W. Hager (2006)

Commentationes Mathematicae Universitatis Carolinae

For Tychonoff X and α an infinite cardinal, let α def X : = the minimum number of α  cozero-sets of the Čech-Stone compactification which intersect to X (generalizing -defect), and let rt X : = min α max ( α , α def X ) . Give C ( X ) the compact-open topology. It is shown that τ C ( X ) n χ C ( X ) rt X = max ( L ( X ) , L ( X ) def X ) , where: τ is tightness; n χ is the network character; L ( X ) is the Lindel"of number. For example, it follows that, for X Čech-complete, τ C ( X ) = L ( X ) . The (apparently new) cardinal functions n χ C and rt are compared with several others.

New metrics for weak convergence of distribution functions.

Michael D. Taylor (1985)

Stochastica

Sibley and Sempi have constructed metrics on the space of probability distribution functions with the property that weak convergence of a sequence is equivalent to metric convergence. Sibley's work is a modification of Levy's metric, but Sempi's construction is of a different sort. Here we construct a family of metrics having the same convergence properties as Sibley's and Sempi's but which does not appear to be related to theirs in any simple way. Some instances are brought out in which the metrics...

New proofs of classical insertion theorems

Chris Good, Ian Stares (2000)

Commentationes Mathematicae Universitatis Carolinae

We provide new proofs for the classical insertion theorems of Dowker and Michael. The proofs are geometric in nature and highlight the connection with the preservation of normality in products. Both proofs follow directly from the Katětov-Tong insertion theorem and we also discuss a proof of this.

New regions of stability in input optimization

Sheng Huang, Sanjo Zlobec (1988)

Aplikace matematiky

using point-to-set mappings we identify two new regions of stability in input optimization. Then we extend various results from the literature on optimality conditions, continuity of Lagrange multipliers, and the marginal value formula over the new and some old regions of stability.

No arc-connected treelike continuum is the 2-to-1 image of a continuum

Jo Heath, Van C. Nall (2003)

Fundamenta Mathematicae

In 1940, O. G. Harrold showed that no arc can be the exactly 2-to-1 continuous image of a metric continuum, and in 1947 W. H. Gottschalk showed that no dendrite is a 2-to-1 image. In 2003 we show that no arc-connected treelike continuum is the 2-to-1 image of a continuum.

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