Question Ejercicio sobre continuidad

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2 years 11 months ago #2239 by Ana_Bernedo
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2 years 11 months ago #2238 by Oscar_Jarrin
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2 years 11 months ago #2237 by Oscar_Jarrin
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2 years 11 months ago #2236 by Oscar_Jarrin
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2 years 11 months ago #2235 by Ana_Bernedo
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2 years 11 months ago #2233 by Oscar_Jarrin
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2 years 11 months ago #2226 by Oscar_Jarrin
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2 years 11 months ago #2224 by Ana_Bernedo
Ejercicio sobre continuidad was created by Ana_Bernedo
Hola, tengo dudas en como resolver este ejercicio, espero pueda guiarme y corregirme :cheer:
Tenemos un espacio métrico (X,d), f:X-->R es continua, "c" pertenece a R.
a) probar usando la definicion de funcion continua que: {x pertenece a X, f(x)<c } y {x pertenece a X, f(x)>c} son conjuntos abiertos.
b) probar usando la equivalencia de continuidad por sucesiones que {x pertenece a X, f(x)<=c } y {x pertenece a X, f(x)>=c} son conjuntos cerrados.

Envio adjunto lo que hice, mi manera de entenderlo graficamente y Pero me parece que estoy entendiendo mal. Espero pueda ayudarme
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