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Topology: An Inquiry-Based Approach

Steven Schlicker

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Section Topological Invariants

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Homeomorphic topological spaces are essentially the same from a topological perspective, and they share many properties, but not all. The properties they share are called topological invariants or topological properties.
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Definition 14.13.

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A property of a topological space X is a topological property (or topological invariant ) if every topological space homeomorphic to X has the same property.
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Activity 14.6.

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Which of the following are topological invariants? That is for topological spaces (X,Ο„X) and (Y,Ο„Y), if X and Y are homeomorphic space and X has the property, does it follow that Y must also have that property?
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