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My question might seem obvious but still I want to sure if the result I shall state below is true:

if the neighborhood base in each point of a space say X is finite. Then we have a discrete topology.

Many thanks and apologies in case I just stated some insanity above :)

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No, this is not true. It would imply, for instance, that every finite topological space is discrete, but this is far from the case. For a trivial example, take the trivial (or indiscrete) topology on any finite set $X$ of cardinality greater than one. Or take the Sierpinski space, i.e., the unique two-point space (up to homeomorphism) with one open point and one closed point.

Thinking about these examples may help you formulate further conditions on your space sufficient for what you want to hold. Hint: think about separation axioms.

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    Thanks for the examples and the hint2011-05-13
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Am I misreading this question? It seems like it's obviously not true, for example any finite non-discrete space.

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    thanks hehehe well that was a rough thought in m$y$ mind and I stated it the way it seemed to me2011-05-13