184:
117:
157:
137:
76:
252:
198:
205:(1950) and Smirnov (1951). Both theorems are often merged in the Bing-Nagata-Smirnov metrization theorem. It is a common tool to prove other
246:
270:
229:
which provides a sufficient condition for metrization, this theorem provides both a necessary and sufficient condition for a
285:
95:. A family of sets is called σ-discrete when it is a union of countably many discrete collections, where a family
214:
210:
162:
98:
226:
206:
17:
266:
230:
43:
92:
84:
202:
142:
122:
61:
279:
79:
234:
47:
39:
249: – A topological vector space whose topology can be defined by a metric
31:
265:"General Topology", Ryszard Engelking, Heldermann Verlag Berlin, 1989.
194:
255: – Characterizes when a topological space is metrizable
168:
104:
159:
has a neighborhood that intersects at most one member of
165:
145:
125:
101:
64:
27:
Characterizes when a topological space is metrizable
197:in 1951 and was an independent discovery with the
178:
151:
131:
111:
70:
8:
58:The theorem states that a topological space
221:Comparison with other metrization theorems
217:is metrizable – is a direct consequence.
209:, e.g. the Moore metrization theorem – a
167:
166:
164:
144:
124:
103:
102:
100:
63:
139:is called discrete, when every point of
201:that was proved independently by both
7:
247:Metrizable topological vector space
78:is metrizable if and only if it is
253:Nagata–Smirnov metrization theorem
199:Nagata–Smirnov metrization theorem
25:
179:{\displaystyle {\mathcal {F}}.}
18:Bing's metrization theorem
112:{\displaystyle {\mathcal {F}}}
1:
302:
193:The theorem was proven by
36:Bing metrization theorem
42:, characterizes when a
180:
153:
133:
119:of subsets of a space
113:
72:
225:Unlike the Urysohn's
211:collectionwise normal
181:
154:
134:
114:
91:and has a σ-discrete
73:
286:Theorems in topology
207:metrization theorems
163:
143:
123:
99:
62:
227:metrization theorem
176:
149:
129:
109:
68:
231:topological space
152:{\displaystyle X}
132:{\displaystyle X}
71:{\displaystyle X}
44:topological space
16:(Redirected from
293:
185:
183:
182:
177:
172:
171:
158:
156:
155:
150:
138:
136:
135:
130:
118:
116:
115:
110:
108:
107:
77:
75:
74:
69:
54:Formal statement
21:
301:
300:
296:
295:
294:
292:
291:
290:
276:
275:
262:
243:
223:
191:
161:
160:
141:
140:
121:
120:
97:
96:
88:
60:
59:
56:
28:
23:
22:
15:
12:
11:
5:
299:
297:
289:
288:
278:
277:
274:
273:
261:
258:
257:
256:
250:
242:
239:
222:
219:
190:
187:
175:
170:
148:
128:
106:
86:
67:
55:
52:
38:, named after
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
298:
287:
284:
283:
281:
272:
271:3-88538-006-4
268:
264:
263:
259:
254:
251:
248:
245:
244:
240:
238:
236:
232:
228:
220:
218:
216:
212:
208:
204:
200:
196:
188:
186:
173:
146:
126:
94:
90:
89:
81:
65:
53:
51:
49:
45:
41:
37:
33:
19:
224:
192:
83:
57:
35:
29:
215:Moore space
260:References
235:metrizable
48:metrizable
40:R. H. Bing
280:Category
241:See also
32:topology
189:History
80:regular
269:
233:to be
203:Nagata
34:, the
93:basis
267:ISBN
195:Bing
82:and
46:is
30:In
282::
237:.
213:,
50:.
174:.
169:F
147:X
127:X
105:F
87:0
85:T
66:X
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.