A compression of digital images derived from a Khalimsky topological structure

Some Properties of Lattice-Based K- And M-Maps

“…then we say that the map f is K-continuous at a point x ∈ X [16,11] if f is continuous at the point x from the viewpoint of K-topology. Furthermore, a map f : X → Y is Khalimsky (K-, for short) continuous if it is K-continuous at every point x ∈ X.…”

“…Furthermore, a map f : X → Y is Khalimsky (K-, for short) continuous if it is K-continuous at every point x ∈ X. By using K-continuous maps, we obtain a category of K-topological spaces, denoted by KTC [11], consisting of the following two sets:…”

“…By using the K-topological graph derived from K-topology, the recent paper [11] developed the so-called A-map (see Definition 13 in the present paper) which is broader than a K-continuous map. This approach can be substantially helpful to study geometric transformations of K-topological spaces (X, κ n X ).…”

“…Using A-maps, we establish the KA-category [11], denoted by KAC, consisting of the following two sets.…”

“…The paper [11] denotes by LAC the category consisting of the following two sets: ( * 1) the set of spaces (X, E n X ) := X as objects of LAC denoted by Ob(LAC); ( * 2) the set of LA-maps of every ordered pair of elements in Ob(LAC) as morphisms of LAC denoted by M or(LAC).…”