Displaying similar documents to “A note on operators extending partial ultrametrics”

A continuous operator extending ultrametrics

I. Stasyuk, Edward D. Tymchatyn (2009)

Commentationes Mathematicae Universitatis Carolinae

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The problem of continuous simultaneous extension of all continuous partial ultrametrics defined on closed subsets of a compact zero-dimensional metric space was recently solved by E.D. Tymchatyn and M. Zarichnyi and improvements to their result were made by I. Stasyuk. In the current paper we extend these results to complete, bounded, zero-dimensional metric spaces and to both continuous and uniformly continuous partial ultrametrics.

The Measurability of Complex-Valued Functional Sequences

Keiko Narita, Noboru Endou, Yasunari Shidama (2009)

Formalized Mathematics

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In this article, we formalized the measurability of complex-valued functional sequences. First, we proved the measurability of the limits of real-valued functional sequences. Next, we defined complex-valued functional sequences dividing real part into imaginary part. Then using the former theorems, we proved the measurability of each part. Lastly, we proved the measurability of the limits of complex-valued functional sequences. We also showed several properties of complex-valued measurable...

Egoroff's Theorem

Noboru Endou, Yasunari Shidama, Keiko Narita (2008)

Formalized Mathematics

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The goal of this article is to prove Egoroff's Theorem [13]. However, there are not enough theorems related to sequence of measurable functions in Mizar Mathematical Library. So we proved many theorems about them. At the end of this article, we showed Egoroff's theorem.MML identifier: MESFUNC8, version: 7.8.10 4.100.1011