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T_1 をテンプレートにして作成
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開始行:
*Definition [#n1085b21]
*Property [#pfee1988]
- A topological space (X,τ) is a T_1 space iff one of the following conditions holds:
++∀x∈X, {x}' is empty. [5]
++∀x∈X, cl({x})={x}. [5]
++∀x,y∈X, &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20x%5cneq%20y%20%5cmbox%7b%20implies%20%7d%20%5crm%7bcl%7d%28%5c%7bx%5c%7d%29%5ccap%5crm%7bcl%7d%28%5c%7by%5c%7d%29=%5cemptyset%20%5c%5d%7d%25.png);. [5]
++Every subset of X is a [[Λ-set]]. [7]
-T_1 = [[T_0]] + [[R_0]]. [2]
-T_1 = [[T_R]] + [[R_0]]. [6]
-T_1 = [[T_0]] + [[C_0]]. [6]
-T_1 ⇒ [[nearly T_1]]. [3]
-T_1 ⇒ [[T_{EF}]]. [4]
-T_1 ⇒ [[λ-T_1]]. [8]
*Reference [#e1ea338c]
+ ???
+Dorsett C., ''Images and hyperspaces of s-essentially T_1 and s-essentially T_2 spaces and semitopological properties.'' (Serbo-Croatian summary) Glas. Mat. Ser. III 21(41) (1986), no. 2, 415–422.
+Przemski M., ''Nearly T_i-continuous functions and some separation axioms.'' (Serbo-Croatian summary), Glas. Mat. Ser. III 21(41) (1986), no. 2, 431–435.
+McSherry D. M. G. , ''On separation axioms weaker than T_1.'' , Proc. Roy. Irish Acad. Sect. A 74 (1974), 115–118.
+Guia Josep, ''Axioms weaker than R0.'', (Serbo-Croatian summary), Mat. Vesnik 36 (1984), no. 3, 195-205.
+Guia Josep, ''Essentially T_D and essentially T_UD spaces.'', Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 32(80) (1988), no. 3, 227-233.
+Arenas Francisco G., Dontchev Julian, Ganster Maximilian, ''On λ-sets and the dual of generalized continuity.'', Questions Answers Gen. Topology 15 (1997), no. 1, 3-13.
+Caldas Miguel, Jafari Saeid, Navalagi Govindappa, ''More on λ-closed sets in topological spaces.'',Rev. Colombiana Mat. 41 (2007), no. 2, 355-369.
終了行:
*Definition [#n1085b21]
*Property [#pfee1988]
- A topological space (X,τ) is a T_1 space iff one of the following conditions holds:
++∀x∈X, {x}' is empty. [5]
++∀x∈X, cl({x})={x}. [5]
++∀x,y∈X, &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20x%5cneq%20y%20%5cmbox%7b%20implies%20%7d%20%5crm%7bcl%7d%28%5c%7bx%5c%7d%29%5ccap%5crm%7bcl%7d%28%5c%7by%5c%7d%29=%5cemptyset%20%5c%5d%7d%25.png);. [5]
++Every subset of X is a [[Λ-set]]. [7]
-T_1 = [[T_0]] + [[R_0]]. [2]
-T_1 = [[T_R]] + [[R_0]]. [6]
-T_1 = [[T_0]] + [[C_0]]. [6]
-T_1 ⇒ [[nearly T_1]]. [3]
-T_1 ⇒ [[T_{EF}]]. [4]
-T_1 ⇒ [[λ-T_1]]. [8]
*Reference [#e1ea338c]
+ ???
+Dorsett C., ''Images and hyperspaces of s-essentially T_1 and s-essentially T_2 spaces and semitopological properties.'' (Serbo-Croatian summary) Glas. Mat. Ser. III 21(41) (1986), no. 2, 415–422.
+Przemski M., ''Nearly T_i-continuous functions and some separation axioms.'' (Serbo-Croatian summary), Glas. Mat. Ser. III 21(41) (1986), no. 2, 431–435.
+McSherry D. M. G. , ''On separation axioms weaker than T_1.'' , Proc. Roy. Irish Acad. Sect. A 74 (1974), 115–118.
+Guia Josep, ''Axioms weaker than R0.'', (Serbo-Croatian summary), Mat. Vesnik 36 (1984), no. 3, 195-205.
+Guia Josep, ''Essentially T_D and essentially T_UD spaces.'', Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 32(80) (1988), no. 3, 227-233.
+Arenas Francisco G., Dontchev Julian, Ganster Maximilian, ''On λ-sets and the dual of generalized continuity.'', Questions Answers Gen. Topology 15 (1997), no. 1, 3-13.
+Caldas Miguel, Jafari Saeid, Navalagi Govindappa, ''More on λ-closed sets in topological spaces.'',Rev. Colombiana Mat. 41 (2007), no. 2, 355-369.
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