Freezing Sets Invariant-based Characteristics of Digital Images

Abstract

Due to the widespread use of digital images of real-world objects as mathematical models, this research examines the freezing sets invariant-base properties of digital images. In contrast to earlier studies that only covered a discrete or limited collection of points, fixed points of digitally continuous functions are approved to deal with a variety of characteristics of digital images.

Remarks on fixed point assertions in digital topology, 5

“…Several papers subsequent to [8] have further developed our knowledge of freezing sets. Such a claim cannot be made for [1]. Below, we quote verbatim (with some corrections noted) each assertion presented as new in [1], with the assertion it mimics from [8].…”

“…Such a claim cannot be made for [1]. Below, we quote verbatim (with some corrections noted) each assertion presented as new in [1], with the assertion it mimics from [8]. Since [8] is cited in [1], the authors of [1] should have known better.…”

“…Theorem 2.4 of [1] reads as follows (note "V is a freezing subset" should be "A is a freezing subset").…”

“…Theorem 3.4 of [1] reads as follows, where " κ 1 , κ 2 " should be "κ 1 , κ 2 " and "p(α 1 , α 2 , . .…”

“…The topic of freezing sets [8] belongs to the fixed point theory of digital topology and is central to the paper [1]. We show that the latter paper contains no original results.…”