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Remarks on sequence-convering closed maps

100%

Tuyen L. Q.

Fasciculi Mathematici

2014

tom Nr 53

161--165

In this paper, we prove that each sequence-covering closed map on spaces with point-countable weak bases is 1-sequence-covering (or weak-open).

Compositions of simple maps

100%

Krzempek J.

Fundamenta Mathematicae

1999

tom 162

nr 2

149-162

A map (= continuous function) is of order ≤ k if each of its point-inverses has at most k elements. Following [4], maps of order ≤ 2 are called simple. Which maps are compositions of simple closed [open, clopen] maps? How many simple maps are really needed to represent a given map? It is proved herein that every closed map of order ≤ k defined on an n-dimensional metric space is a composition of (n+1)k-1 simple closed maps (with metric domains). This theorem fails to be true for non-metrizable spaces. An appropriate map on a Cantor cube of uncountable weight is described.

Another approach to dimension of maps

84%

Krzempek J.

2002

tom Vol. 50, no 2

141-154

Two equivalent definitions of the Cech-Lebesgue dimension are extended to closed (continuous) maps. This leads to two different dimension-like functions: the covering dimension and partition dimension of maps. A few characterizations of at most n-dimensional maps (for both dimensions) are proved as well as countable and locally finite sum theorems.

The Idzik type quasivariational inequalities and noncompact optimization problems

84%

Park S. , Park J. A.

Colloquium Mathematicum

1996

tom 71

nr 2

287-295