Category:Characterization of Paracompactness in T3 Space
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This category contains pages concerning Characterization of Paracompactness in T3 Space:
Let $T = \struct {X, \tau}$ be a $T_3$ space.
The following statements are equivalent:
- $(1): \quad T$ is paracompact
- $(2): \quad$ every open cover of $T$ has a locally finite refinement
- $(3): \quad$ every open cover of $T$ has a closed locally finite refinement
- $(4): \quad$ every open cover of $T$ is even
- $(5): \quad$ every open cover of $T$ has an open $\sigma$-discrete refinement
- $(6): \quad$ every open cover of $T$ has an open $\sigma$-locally finite refinement
Pages in category "Characterization of Paracompactness in T3 Space"
The following 30 pages are in this category, out of 30 total.
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- Characterization of Paracompactness in T3 Space
- Characterization of Paracompactness in T3 Space/Lemma 1
- Characterization of Paracompactness in T3 Space/Lemma 10
- Characterization of Paracompactness in T3 Space/Lemma 11
- Characterization of Paracompactness in T3 Space/Lemma 12
- Characterization of Paracompactness in T3 Space/Lemma 13
- Characterization of Paracompactness in T3 Space/Lemma 14
- Characterization of Paracompactness in T3 Space/Lemma 15
- Characterization of Paracompactness in T3 Space/Lemma 16
- Characterization of Paracompactness in T3 Space/Lemma 17
- Characterization of Paracompactness in T3 Space/Lemma 18
- Characterization of Paracompactness in T3 Space/Lemma 19
- Characterization of Paracompactness in T3 Space/Lemma 2
- Characterization of Paracompactness in T3 Space/Lemma 20
- Characterization of Paracompactness in T3 Space/Lemma 21
- Characterization of Paracompactness in T3 Space/Lemma 3
- Characterization of Paracompactness in T3 Space/Lemma 4
- Characterization of Paracompactness in T3 Space/Lemma 5
- Characterization of Paracompactness in T3 Space/Lemma 6
- Characterization of Paracompactness in T3 Space/Lemma 7
- Characterization of Paracompactness in T3 Space/Lemma 8
- Characterization of Paracompactness in T3 Space/Lemma 9
- Characterization of Paracompactness in T3 Space/Statement 1 implies Statement 2
- Characterization of Paracompactness in T3 Space/Statement 1 implies Statement 6
- Characterization of Paracompactness in T3 Space/Statement 2 implies Statement 3
- Characterization of Paracompactness in T3 Space/Statement 3 implies Statement 1
- Characterization of Paracompactness in T3 Space/Statement 3 implies Statement 4
- Characterization of Paracompactness in T3 Space/Statement 4 implies Statement 5
- Characterization of Paracompactness in T3 Space/Statement 5 implies Statement 6
- Characterization of Paracompactness in T3 Space/Statement 6 implies Statement 2