FT_2-fuzzy supercompact spaces, fuzzy compact finite spaces and infinite fuzzy compact net spaces

摘要

Following questions of classical case have been answered under fuzzy setting: Question 1. Whether Hausdorff continuous images of supercompact Hausdorff spaces are supercompact? Question 2. Is there a non-supercompact Hausdorff space which is a continuous image of some supercompact Hausdorff space? Question 3. Whether X * Y supercompact implies that X and Y are supercompact? Question 4. Is there a non-supercompact Hausdorff space X and a Hausdorff space Y such that X * Y is supercompact? Question 5. Is a closed G_g-subspace of a supercompact Hausdorff space supercompact? Fuzzy compact finite spaces and infinite fuzzy compact net spaces have also been introduced.