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On strict and simple type extensions
1998
International Journal of Mathematics and Mathematical Sciences
Let(Y,τ)be an extension of a space(X,τ′)⋅p∈Y, let𝒪yp={W∩X:W∈τ,p∈W}. ForU∈τ′, leto(U)={P∈Y:U∈𝒪yp}. In 1964, Banaschweski introduced the strict extensionY#, and the simple extensionY+ofX(induced by(Y,τ)) having base{o(U):U∈τ′}and{U∪{p}:p∈Y,and U∈Oyp}, respectively. The extensionsY#andY+have been extensively used since then. In this paper, the open filtersℒp={W∈τ′:W⫆intxclx(U)for someU∈𝒪yp}, and𝒰p={W∈τ′:intxclx(W)∈𝒪yp}={W∈τ′:intxclx(W)∈ℒp}=∩{𝒰:𝒰is an open ultrafilter onX,𝒪yp⊂𝒰}onXare used to
doi:10.1155/s0161171298000349
fatcat:mdvenf3iqfc7rdbh7mn3zk7hbq