We hope you enjoy our website created to show attractiveness of Math.

by Jens Bossaert (Curiosa Mathematica on Tumblr.com)

by Michael Zarichnyi

by Jens Bossaert (Curiosa Mathematica on Tumblr.com)

by Jens Bossaert (Curiosa Mathematica on Tumblr.com)

by Michael Zarichnyi

The Kakutani fixed-point theorem is a fixed-point theorem for set-valued functions. Let S be a non-empty, compact and convex subset of some Euclidean space. If f is a convex-valued self-map of S with closed graph, then f has a fixed point.

by Michael Zarichnyi

Given a solid ball in 3-dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball. This can be also proved for another bounded domains in 3-dimensional space.

by Michael Zarichnyi

by Michael Zarichnyi

Banach-Schauder theorem (open mapping theorem). If a continuous linear operator between Banach spaces is surjective then it is an open map.

by Michael Zarichnyi

Banach contraction principle. Every contraction in a complete metric space has a unique fixed point.

by Michael Zarichnyi

Hahn-Banach theorem, in its geometric form, states that any two disjoint closed convex sets (at least one of them is assumed to be compact) in a locally conves space can be separated with a hyperplane.

by Michael Zarichnyi

Banach-Mazur distance. This is a distance on the set of [isometry classes of] n-dimensional normed spaces.

by Taras Banakh

by Michael Zarichnyi

by Michael Zarichnyi

by Michael Zarichnyi

by Michael Zarichnyi

by Michael Zarichnyi

A fiber bundle (or, in British English, fibre bundle) is a space that is locally a product space, but globally may have a different topological structure.

by Michael Zarichnyi

by Michael Zarichnyi

Fuzzy sets (aka uncertain sets) are somewhat like sets whose elements have degrees of membership; this is described with the aid of a membership function valued in the real unit interval [0, 1].

by Michael Zarichnyi

by Michael Zarichnyi

by Michael Zarichnyi

A class of objects or methods exhibit recursive behavior when they can be defined by two properties: 1) A simple base case (or cases)-a terminating scenario that does not use recursion to produce an answer. 2) A set of rules that reduce all other cases toward the base case.

by Michael Zarichnyi

Real trees (also called R-trees) are a class of metric spaces generalizing simplicial trees. A metric space is a real tree if it is a geodesic space where every triangle is a tripod.

by Michael Zarichnyi

A solenoid is a compact connected topological space (i.e. a continuum) that may be obtained as the inverse limit of an inverse system of topological groups (e.g., circles) and continuous homomorphisms (e.g., squarings).

Michael Zarichnyi is a professor of mathematics at the Lviv University (Ukraine) and Rzeszow University (Poland). His interests include not only geometry and topology of infinite-dimensional manifolds but also poetry, music and visual poetry. He is the authour of 3 books of poetry, about 100 songs, a large number of visual works.