Let S be a nonorientable surface. A collection of pairwise noncrossing simple closed curves in S is a blockage if every onesided simple closed curve in S crosses at least one of them. Robertson and Thomas [9] conjectured that the orientable genus of any graph G embedded in S with sufficiently large face-width is “roughly” equal to one half of the minimum number of intersections of a blockage wi...

Let S be a nonorientable surface. A collection of pairwise noncross-ing simple closed curves in S is a blockage if every onesided simple closed curve in S crosses at least one of them. Robertson and Thomas 9] conjectured that the orientable genus of any graph G embedded in S with suuciently large face-width is \roughly" equal to one half of the minimum number of intersections of a blockage with...

We introduce the class of linearly S-closed spaces as a proper subclass H-closed spaces. This property lies between S-closedness and countable S-closedness. A space is called if only any semi-open chain cover posses member dense in space. It shown that extremally disconnected coincide. gave characterizations these terms s-accumulation points filter bases complete families open subsets. While re...