Nonexistence of linear operators extending Lipschitz (pseudo)metric

We present an example of a zero-dimensional compact metric space $X$ and its closed subspace $A$ such that there is no continuous linear extension operator for the Lipschitz pseudometrics on $A$ to the Lipschitz pseudometrics on $X$. The construction is based on results of A. Brudnyi and Yu. Brudnyi concerning linear extension operators for Lipschitz functions.Comment: arXiv admin note: substantial text overlap with arXiv:math/040820

There is no universal proper metric spaces for asymptotic dimension 1

Answering a question of Ma, Siegert, and Dydak we show that there is no universal proper metric space for the asymptotic dimension $n\ge1$.Comment: 3 page

Strong topology on the set of persistence diagrams

We endow the set of persistence diagrams with the strong topology (the topology of countable direct limit of increasing sequence of bounded subsets considered in the bottleneck distance). The topology of the obtained space is described. Also, we prove that the space of persistence diagrams with the bottleneck metric has infinite asymptotic dimension in the sense of Gromov.Comment: 6 page

Max-min measures on ultrametric spaces

The ultrametrization of the set of all probability measures of compact support on the ultrametric spaces was first defined by Hartog and de Vink. In this paper we consider a similar construction for the so called max-min measures on the ultrametric spaces. In particular, we prove that the functors max-min measures and idempotent measures are isomorphic. However, we show that this is not the case for the monads generated by these functors

On some aspects of the set theory and topology in J. Puzyna’s monumental work

The article highlights certain aspects of the set theory and topology in Puzyna’s work Theory of analytic functions (1899, 1900). In particular, the following notions are considered: derivative of a set, cardinality, connectedness, accumulation point, surface, genus of surface

On the beginning of topology in Lwów

We provide one of the first surveys of results in the area of topology by representatives of the Lvov School of mathematics and mathematicians related to the University of Lvov. Viewed together, these results show the importance of this school in the creation of topology

Lwów period of S. Ulam’s mathematical creativity

We provide an outline of Stanisław Ulam’s results obtained in the framework of the widely understood Lvov school of mathematics