Closed and basic closed C*D-filters are used in a process similar to Wallman method for compactifications of the topological spaces Y, of which, there is a subset of C*(Y) containing a non-constant function, where C*(...Closed and basic closed C*D-filters are used in a process similar to Wallman method for compactifications of the topological spaces Y, of which, there is a subset of C*(Y) containing a non-constant function, where C*(Y) is the set of bounded real continuous functions on Y. An arbitrary Hausdorff compactification (Z,h) of a Tychonoff space X can be obtained by using basic closed C*D-filters from in a similar way, where C(Z) is the set of real continuous functions on Z.展开更多
定义1 广义拓扑空间 X 称为 W 型的当且仅当它满足附加条件:[W]a∧b=0a∩b=0.易见不分明拓扑空间与拓扑空间都是 W 型的。但一致空间与接近空间却不是 W 型的。因为,如设 A=expX-{φ,X},B={φ,X},则A∧B=cxpX但 A≮B°.W 型的广义...定义1 广义拓扑空间 X 称为 W 型的当且仅当它满足附加条件:[W]a∧b=0a∩b=0.易见不分明拓扑空间与拓扑空间都是 W 型的。但一致空间与接近空间却不是 W 型的。因为,如设 A=expX-{φ,X},B={φ,X},则A∧B=cxpX但 A≮B°.W 型的广义拓扑空间的范畴记为 Wts。显然,Fts 与 Top 都是 Wts 的满子范畴,而Wts 则是 Gts 的满子范畴。展开更多
This paper deals with spaces such that their compactification is a resolvable space. A characterization of space such that its one point compactification (resp. Wallman compactification) is a resolvable space is given.
By means of a characterization of compact spaces in terms of open CD*-filters induced by a , a - and open CD*-filters process of compactifications of an arbitrary topological space Y is obtained in Sec. 3 by embedding...By means of a characterization of compact spaces in terms of open CD*-filters induced by a , a - and open CD*-filters process of compactifications of an arbitrary topological space Y is obtained in Sec. 3 by embedding Y as a dense subspace of , YS = {ε |ε is an open CD*-filter that does not converge in Y}, YT = {A|A is a basic open CD*-filter that does not converge in Y}, is the topology induced by the base B = {U*|U is open in Y, U ≠φ} and U* = {F∈Ysw (or YTw)|U∈F}. Furthermore, an arbitrary Hausdorff compactification (Z, h) of a Tychonoff space X?can be obtained from a by the?similar process in Sec.3.展开更多
In this note,we prove that the Banaschewski-Mulvey's compact regular reflection construction of locales is isomorphic to the Johnstone Wallman compcactification of locales. We show that a subfit semi-normal locale...In this note,we prove that the Banaschewski-Mulvey's compact regular reflection construction of locales is isomorphic to the Johnstone Wallman compcactification of locales. We show that a subfit semi-normal locale is normal,but the converse is not true in general. Furthermore,we generalize the main result in[4].展开更多
文摘Closed and basic closed C*D-filters are used in a process similar to Wallman method for compactifications of the topological spaces Y, of which, there is a subset of C*(Y) containing a non-constant function, where C*(Y) is the set of bounded real continuous functions on Y. An arbitrary Hausdorff compactification (Z,h) of a Tychonoff space X can be obtained by using basic closed C*D-filters from in a similar way, where C(Z) is the set of real continuous functions on Z.
文摘定义1 广义拓扑空间 X 称为 W 型的当且仅当它满足附加条件:[W]a∧b=0a∩b=0.易见不分明拓扑空间与拓扑空间都是 W 型的。但一致空间与接近空间却不是 W 型的。因为,如设 A=expX-{φ,X},B={φ,X},则A∧B=cxpX但 A≮B°.W 型的广义拓扑空间的范畴记为 Wts。显然,Fts 与 Top 都是 Wts 的满子范畴,而Wts 则是 Gts 的满子范畴。
文摘This paper deals with spaces such that their compactification is a resolvable space. A characterization of space such that its one point compactification (resp. Wallman compactification) is a resolvable space is given.
文摘By means of a characterization of compact spaces in terms of open CD*-filters induced by a , a - and open CD*-filters process of compactifications of an arbitrary topological space Y is obtained in Sec. 3 by embedding Y as a dense subspace of , YS = {ε |ε is an open CD*-filter that does not converge in Y}, YT = {A|A is a basic open CD*-filter that does not converge in Y}, is the topology induced by the base B = {U*|U is open in Y, U ≠φ} and U* = {F∈Ysw (or YTw)|U∈F}. Furthermore, an arbitrary Hausdorff compactification (Z, h) of a Tychonoff space X?can be obtained from a by the?similar process in Sec.3.
基金the National Natural Science Foundation of China （No. 10331010）.
文摘In this note,we prove that the Banaschewski-Mulvey's compact regular reflection construction of locales is isomorphic to the Johnstone Wallman compcactification of locales. We show that a subfit semi-normal locale is normal,but the converse is not true in general. Furthermore,we generalize the main result in[4].
