Textures and -spaces

Plain ditopological texture spaces

“…We begin by recalling the result of Demirci mentioned in the introduction. It is established in [9] that if (N, ) In terms of the interior relation ω of L N [2] this gives mωn ⇐⇒ P n Q m ⇐⇒ P m ⊆ P n ⇐⇒ m ∈ P n ⇐⇒ m n, so ω coincides with . As pointed out in [9], the corresponding C -space (N, L c N ) is in fact an Alexandroff discrete [15],…”

“…In [9], Mustafa Demirci pointed out that plain textures may be characterized in terms of partially ordered sets (posets). In this paper we take up this topic in greater detail, and present several important new results relating to plain textures and plain ditopological texture spaces.…”

Α - Open Sets and Α - Bicontinuity in Ditopological Texture Spaces

“…Textures were introduced by L. M. Brown as a point-set for the study of fuzzy sets, but they have since proved useful as a framework in which to discuss complement free mathematical concepts. In this section we recall some basic notions regarding textures and ditopologies, and an adequate introduction to the theory and the motivation for its study may be obtained from [1,2,3,4,5,6,7].…”

Real dicompactifications of ditopological texture spaces

“…However, as noted in [3,14] we may associate with (S, S) the C-space [15] (core-space) (S, S c ), and then the frequently occurring relationship P s Q s , s, s ∈ S, is equivalent to s ω S s , where ω S is the interior relation for (S, S c ). In particular if (S, S), (T , T) are textures and ϕ : S → T a point function, then ϕ is called ω-preserving if s 1 ω S s 2 ⇒ ϕ(s 1 ) ω T ϕ(s 2 ).…”