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# Topology Fundamentals Quiz

### 1. Which of the following statements correctly defines a topological space?

### 2. What property does a continuous function between two topological spaces preserve?

### 3. Which topological property is defined by the absence of separable disjoint non-empty open sets?

### 4. Which statement is true about compact sets in a topological space?

### 5. Identify the concept that describes when two topological spaces are equivalent in a topological sense.

### 6. In topology, a space is said to be Hausdorff if which of the following conditions is met?

### 7. What is the primary characteristic of a metric space?

### 8. A function between topological spaces is considered open if it maps open sets to

### 9. Which of the following is NOT a property of continuous functions in topology?

### 10. The concept of a basis for a topology on a set X is most closely related to which of the following definitions?