Ordinary smooth filters
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First, we define an ordinary smooth filter and obtain its some properties. In particular, we obtain the necessary and sufficient condition of an ordinary smooth filter (See Theorem 3.9). Second, we define an ordinary smooth filter base (See Theorem 4.1). Third, we introduce the concept of an ordinary smooth ultrafilter and study its some properties. Moreover, we obtain the necessary and sufficient condition of an induced ordinary smooth filter (See Theorem 5.8). Fourth, we define the image and the inverse image of an ordinary smooth filter. Finally, we introduce level set and strong level set of an ordinary smooth filter and obtain their some properties.
Abstract
First, we define an ordinary smooth filter and obtain its some properties. In particular, we obtain the necessary and sufficient condition of an ordinary smooth filter (See Theorem 3.9). Second, we define an ordinary smooth filter base (See Theorem 4.1). Third, we introduce the concept of an ordinary smooth ultrafilter and study its some properties. Moreover, we obtain the necessary and sufficient condition of an induced ordinary smooth filter (See Theorem 5.8). Fourth, we define the image and the inverse image of an ordinary smooth filter. Finally, we introduce level set and strong level set of an ordinary smooth filter and obtain their some properties.
참고문헌 (20)
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