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Submaximality, Extremal Disconnectedness and Generalized
... considerable interest among general topologists. One reason is these objects are natural generalizations of closed sets. More importantly, generalized closed sets suggest some new separation axioms which have been found to be very useful in the study of certain objects of digital topology, for examp ...
... considerable interest among general topologists. One reason is these objects are natural generalizations of closed sets. More importantly, generalized closed sets suggest some new separation axioms which have been found to be very useful in the study of certain objects of digital topology, for examp ...
Houston Journal of Mathematics
... (2) 3 (3). Let D be a r-dense subset of X. Then X \ D is preclosed in (X, T), and so is sg-closed. Therefore, D is sg-open and (X,7) is sg-submaximal. ...
... (2) 3 (3). Let D be a r-dense subset of X. Then X \ D is preclosed in (X, T), and so is sg-closed. Therefore, D is sg-open and (X,7) is sg-submaximal. ...
For the Oral Candidacy examination, the student is examined in
... For the Oral Candidacy examination, the student is examined in three basic subjects (satisfying the requirements of the student's intended Track of Specialization). For each subject, the student must master all of the topics listed on the syllabus. The student is expected to have a through understan ...
... For the Oral Candidacy examination, the student is examined in three basic subjects (satisfying the requirements of the student's intended Track of Specialization). For each subject, the student must master all of the topics listed on the syllabus. The student is expected to have a through understan ...
IOSR Journal of Mathematics (IOSR-JM)
... f −1 f(U) ⊆ X − U and X − U is τi - closed. By hypothesis, there exists an i, j -δI -semi-closed set H of Y containing W such that f −1 H ⊆ X − U. Then we have f −1 H ∩ U = ϕ and H ∩ f U = ϕ. Therefore we obtain Y − f U ⊇ H ⊇ W = Y − f U and f U is i, j -δI -semi-open in Y. This shows that f is p -δ ...
... f −1 f(U) ⊆ X − U and X − U is τi - closed. By hypothesis, there exists an i, j -δI -semi-closed set H of Y containing W such that f −1 H ⊆ X − U. Then we have f −1 H ∩ U = ϕ and H ∩ f U = ϕ. Therefore we obtain Y − f U ⊇ H ⊇ W = Y − f U and f U is i, j -δI -semi-open in Y. This shows that f is p -δ ...
Dcpo-completion of posets - Mathematics and Mathematics Education
... any Scott continuous mapping g: P → Q from P into a local dcpo Q, there is a unique Scott continuous mapping g*: S → Q such that g=g*f. ...
... any Scott continuous mapping g: P → Q from P into a local dcpo Q, there is a unique Scott continuous mapping g*: S → Q such that g=g*f. ...