Multivalued functions in digital topology
Project no. 20333 · Status: Kapanmış · 2019
Summary
In this thesis, some digital minimal simple surfaces are constructed by the connected sum of two digital surfaces. The digital simplicial homology groups of these digital surfaces are determined. The Euler characteristics of certain digital connected sum surfaces are computed and some properties are stated on these digital surfaces. In the fourth part of the thesis, the smash product is introduced for digital images. It is shown that this operator is associative, distributive and commutative. A digital suspension and a digital cone of a digital image are defined by this operator. In the fifth section, the digital singular cohomology groups of the digital spaces equipped with Khalimsky topology are studied. Eilenberg-Steenrod axioms, universal coefficient theorem and Künneth formula are investigated for this cohomology theory. The cup product is constructed on Khalimsky topology and some properties of this operation are given. In the last section of the thesis, the approximate fixed point property is defined between digital multivalued functions. The notion of universal digital multivalued function is stated. Some properties of smash product are introduced. Finally, it is shown that some morphological operators have strong and weak continuity.