Displaying similar documents to “A continuous operator extending ultrametrics”

A note on operators extending partial ultrametrics

Edward D. Tymchatyn, Michael M. Zarichnyi (2005)

Commentationes Mathematicae Universitatis Carolinae

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We consider the question of simultaneous extension of partial ultrametrics, i.e. continuous ultrametrics defined on nonempty closed subsets of a compact zero-dimensional metrizable space. The main result states that there exists a continuous extension operator that preserves the maximum operation. This extension can also be chosen so that it preserves the Assouad dimension.

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...

Implicit functions from locally convex spaces to Banach spaces

Seppo Hiltunen (1999)

Studia Mathematica

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We first generalize the classical implicit function theorem of Hildebrandt and Graves to the case where we have a Keller C Π k -map f defined on an open subset of E×F and with values in F, for E an arbitrary Hausdorff locally convex space and F a Banach space. As an application, we prove that under a certain transversality condition the preimage of a submanifold is a submanifold for a map from a Fréchet manifold to a Banach manifold.

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