A Study of Cech Closure Spaces
T A Sunitha, T Thrivikraman · Dyuthi Digital Repository (Cochin University of Science and Technology) · 1994
an A-space.However considering universal acceptability we call the former Cech closure spaces and the latter monotone spaces.In 1978, C.Calude and M.Malitza also mentioned [C-M] the concept ofa total v v Cech space and a total Kuratowski space.A total Cech space [respectively total Kuratoswski space] is a closure space [ respectively Kuratoswski closure space] which also satisfies the condition c(U A) = U c(A) [respectively cl (U A) = U cl (A)].iEI iEI iEI iEI v Calude and Cazanescu mentioned that [C-C] total Cech spaces are in one-to-one, onto v correspondence with reflexive relations and they also studied the category of total Cech spaces and its full subcategory determined by total Kuratowski spaces.TIle ideas about the concepts of a continuous mapping and of a set endowed with continuous operations (compositions) play a fundamental role in general mathematical analysis.Analogous to the notion of the continuity, we consider the v morphisms throughout this thesis.Cech described continuity in closure spaces by means of neighbourhoods, nets etc. Koutnik studied the convergence in non Hausdorff closure space [KOJ He studied more about sequential convergence structure in [K02],[K0l].Mashour and Ghanim in 1982 defined [MA-G)] C-almost continuous as a function fX-->Y, where X and Y are closure spaces and is said to be a C-almost continuous if for each xEX and each V c Y with f{x) E VO, there is U C X such that x E U" and f{U)C( c(U)t They also studied some results related to this concept.D.R.Andrew and E.K.Whittlesy [A-W] and lames Chew [CHE] studied about closure continuity.D.N.Roth and lW.Carlson mentioned [RD-C] the degree of a closure operator.They