| 21. | As a topological space, the real numbers are separable.
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| 22. | Yet this structure barely differs from the model structure over topological spaces.
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| 23. | An arbitrary union of open sets in a topological space is open.
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| 24. | ErdQs space is a totally disconnected, one-dimensional topological space.
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| 25. | In general topological spaces, there is no notion of nearness or distance.
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| 26. | Conversely, there are Grothendieck topologies which do not come from topological spaces.
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| 27. | The homeomorphisms form an equivalence relation on the class of all topological spaces.
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| 28. | This finally motivates the definitions for general topological spaces.
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| 29. | A curve is a topological space which is locally homeomorphic to a line.
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| 30. | Thus generalized topological spaces are equivalent to interior algebras.
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