Universal Spaces for $(k, \overline{k})-$ Surfaces

Generalized Simple Surface Points

“…As a consequence of the well-known Jordan-Brouwer theorem one gets the following separation result; see [5].…”

“…This section collects the terminology and main results from [5] needed in this paper. They are established within the framework for Digital Topology introduced in [1], where we refer to for the precise definitions in a general setting.…”

“…They are established within the framework for Digital Topology introduced in [1], where we refer to for the precise definitions in a general setting. The reader should be aware that some of the material referred to [5] and [1] has been restated here in terms of the notation introduced in Section 2.…”

“…Nevertheless, one particular among them, the so-called universal (k, k)-space, (R 3 , f kk ), captures the essence of all digital surfaces for the pair (k, k). More precisely, the main result in [5] states that any digital surface in a (k, k)-space is also a digital surface in (R 3 , f kk ). Next we recall the definition of the lighting functions f kk and some immediate properties.…”

“…digital topology in [1]. More precisely, we will use crucially the fact that the (k, k)-surfaces in [3] are exactly the strong separating surfaces of certain universal digital space in the sense of [1]; see [5].…”