Wykłady z topologii : zbiory spójne i kontinua

Abstract

The book consists of eight lectures concerning the theory of connectedness and continua to be used as Univeristy text. In the part of the book devoted to continua such topics as Moore theorem concerning cut points, Hahn—Mazurkiewicz, Mazurkiewicz—Moore and Sierpiński theorems concerning locally connected metric continua, theorems on indecomposable continua including Mazurkiewicz theorem on the number of composants are treated. The constructions of some solenoidal continua are given. A lecture is devoted to the non-metric branch of the theory of continua with theorems by Kurepa, Mardešić, Papić and Treybig. There is a special lecture devoted to Peano maps. Some peculiarities among non-compat connected sets are discussed, in particular those which concern biconnected sets. The next is aimed at students at various levels. Some parts are written for more advanced readers.