In this paper, the concept of countable compactness degree and the concept of Lindelof property degree are defined in L-fuzzy topological spaces by means of implication operator → Many properties of them are discussed.
In the paper [properties defined with semi-continuous functions and some related spaces＇, Houston J. Math., 2015, 41（3）： 1097-1106] properties （UL）m^wl, （UL）mK and （UL）m were defined and it was shown that sp...In the paper [properties defined with semi-continuous functions and some related spaces＇, Houston J. Math., 2015, 41（3）： 1097-1106] properties （UL）m^wl, （UL）mK and （UL）m were defined and it was shown that spaces having these properties coincide with countably paracompact spaces, countably mesocompact spaces and countably metacompact spaces, respectively. In this paper, we continue with the study on the relationship between properties defined with real-valued functions and some covering properties. Some characterizations of countably compact spaces and pseudo-compact spaces in terms of real-valued functions are obtained.展开更多
In the framework of topological vector spaces, we give a characterization of strong Minkowski separation, introduced by Cheng, et al., in terms of convex body separation. From this, several results on strong Minkowski...In the framework of topological vector spaces, we give a characterization of strong Minkowski separation, introduced by Cheng, et al., in terms of convex body separation. From this, several results on strong Minkowski separation are deduced. Using the results, we prove a drop theorem involving weakly countably compact sets in locally convex spaces. Moreover, we introduce the notion of the co-drop property and show that every weakly countably compact set has the co-drop property. If the underlying locally convex space is quasi-complete, then a bounded weakly closed set has the co-drop property if and only if it is weakly countably compact.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11471297)
文摘In this paper, the concept of countable compactness degree and the concept of Lindelof property degree are defined in L-fuzzy topological spaces by means of implication operator → Many properties of them are discussed.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1140126211271178)
文摘In the paper [properties defined with semi-continuous functions and some related spaces＇, Houston J. Math., 2015, 41（3）： 1097-1106] properties （UL）m^wl, （UL）mK and （UL）m were defined and it was shown that spaces having these properties coincide with countably paracompact spaces, countably mesocompact spaces and countably metacompact spaces, respectively. In this paper, we continue with the study on the relationship between properties defined with real-valued functions and some covering properties. Some characterizations of countably compact spaces and pseudo-compact spaces in terms of real-valued functions are obtained.
基金National Natural Science Foundation of China(10571035)
文摘In the framework of topological vector spaces, we give a characterization of strong Minkowski separation, introduced by Cheng, et al., in terms of convex body separation. From this, several results on strong Minkowski separation are deduced. Using the results, we prove a drop theorem involving weakly countably compact sets in locally convex spaces. Moreover, we introduce the notion of the co-drop property and show that every weakly countably compact set has the co-drop property. If the underlying locally convex space is quasi-complete, then a bounded weakly closed set has the co-drop property if and only if it is weakly countably compact.
