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Historical remarks on equivalence of functions

Lipecki Z.

Bulletin of the Polish Academy of Sciences. Mathematics

2017

Vol. 65, no. 1

93--95

A theorem of E. Szpilrajn (Marczewski) (1936) on equivalent functions is recalled and its relation to subsequent results published by M. Morayne and C. Ryll-Nardzewski (1999) and M. Kysiak (2005) is briefly discussed.

Uniqueness of Cartesian Products of Compact Convex Sets

Lipecki Z., Losert V., Spurný J.

Bulletin of the Polish Academy of Sciences. Mathematics

2011

Vol. 59, no 2

175--183

Let Xi, i∈I, and Yj, j∈J, be compact convex sets whose sets of extreme points are affinely independent and let φ be an affine homeomorphism of ∏i∈IXi onto ∏j∈JYj. We show that there exists a bijection b:I→J such that φ is the product of affine homeomorphisms of Xi onto Yb(i), i∈I.

Anzelm Iwanik (1946-1998)

Byczkowski T., Downarowicz T., Lipecki Z., Romanowicz Z.

Roczniki Polskiego Towarzystwa Matematycznego. Seria 2: Wiadomości Matematyczne

1999

[Z] 35

191-200

Noncontinuous linear operators and independent linear topologies

Lipecki Z.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1998

[Z] 38

53-62

We establish the existence of badly noncontinuous injective linear operators, isomorphisms and involutions between topological linear spaces. As an application, a metrizable linear topology independent of a given one is exhibited.