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Dear all,<br>
<br>
there is a *change in the room and time* for the announced lecture
at the seminar Set Theory and Analysis! We will meet on<br>
<br>
Tuesday, 19 May 2026, *10:15--11:45*<br>
in the *Blue lecture room* in the *rear building*.<br>
<br>
Best wishes,<br>
Adam<br>
<br>
<br>
<div class="moz-cite-prefix">Dne 16.05.2026 v 9:00 <a class="moz-txt-link-abbreviated" href="mailto:kubis@math.cas.cz">kubis@math.cas.cz</a>
napsal(a):<br>
</div>
<blockquote type="cite"
cite="mid:6746b36590456c1dd825b18b280b33b4@math.cas.cz">
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<title>Set Theory and Analysis</title>
<p> Tuesday, 19 May 2026 - 10:00 to 11:30 <br>
Place: IM, konírna </p>
<p> Speaker: Yoël Perreau, University of Tartu, Estonia<br>
Title: Points of continuity in Lipschitz free-spaces </p>
<p class="ql-ed"> Abstract <br>
</p>
<p>In this talk, I would like present a metric characterization of
points of continuity among molecules in Lipschitz free-spaces.
Recall that a point $x$ on the unit sphere of a Banach space $X$
is said to be a point of weak-to-norm continuity of $B_X$, or
simply a \emph{point of continuity}, if the identity mapping
$Id:(B_X,w)\to (B_X,\norm{\cdot})$ is continuous at $x$. Also
recall that given any complete metric space $M$, the
\emph{Lipschitz free-space} $\lipfree{M}$ of $M$ is a Banach
space which contains an isometric copy of $M$ in a canonical way
and satisfies the following linearization property: given any
Lipschitz map $f:M\to\R$, there exist a unique functional $g$ on
$\lipfree{M}$ such that $g\circ \delta=f$ and
$\norm{g}=\Lip(f)$, where $\delta:M\to \lipfree{M}$ is the
canonical isometric embedding. A \emph{molecule} is an element
of $\lipfree{M}$ of the form
$m_{xy}:=\frac{\delta(x)-\delta(y)}{d(x,y)}$ where $x$ and $y$
are two distinct points in $M$. Molecules act on Lipschitz
functions by computing slopes, and are the simplest possible
elements that one can find in the sphere of a Lipschitz
free-space. I will discuss how to relate the fact that a
molecule $m_{xy}$ is a point of continuity to some local
compactness of the metric space $M$ around the metric segment
between the points $x$ and $y$ as well as a lack of
connectability between these points. If time permits, I will
also explain how this characterization can be extended to
finitely supported elements in $\lipfree{M}$.</p>
<p> For more information see the seminar web page at <br>
<a class="moz-txt-link-freetext" href="https://www.math.cas.cz/index.php/events/seminar/6">https://www.math.cas.cz/index.php/events/seminar/6</a> </p>
<p> Set Theory and Analysis mailing list <br>
<a class="moz-txt-link-abbreviated" href="mailto:settfa@math.cas.cz">settfa@math.cas.cz</a> <br>
<a class="moz-txt-link-freetext" href="https://list.math.cas.cz/listinfo/settfa@math.cas.cz">https://list.math.cas.cz/listinfo/settfa@math.cas.cz</a> </p>
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<pre wrap="" class="moz-quote-pre">_______________________________________________
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</pre>
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