Some traits for S174

spaces/S000174/properties/P000023.md

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+---
+space: S000174
+property: P000023
+value: false
+---
+
+The point $(\omega, \omega, \dots) \in X$ has no compact neighborhood.

spaces/S000174/properties/P000026.md

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+---
+space: S000174
+property: P000026
+value: false
+---
+
+Let $N$ be a countable subset of $X$. Let $r := \sup \{x_0 \mid x \in N\}$. Then the point $(r + 1,0,0,\dots)$ has the neighborhood $\{r + 1\} \times \omega_1^\omega$ which is disjoint with $N$, so $N$ is not dense. 

spaces/S000174/properties/P000048.md

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+---
+space: S000174
+property: P000048
+value: true
+---
+
+Let 

spaces/S000174/properties/P000051.md

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+---
+space: S000174
+property: P000051
+value: false
+---
+
+The subspace $2 ^ \omega \setminus \{(0,0,\dots)\} \subseteq X$ has no isolated point.

spaces/S000174/properties/P000058.md

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+---
+space: S000174
+property: P000058
+value: false
+---
+
+$|X|=|\omega_1^\omega| \geq |2^\omega| = \mathfrak{c}$

spaces/S000174/properties/P000093.md

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+---
+space: S000174
+property: P000093
+value: false
+---
+
+The point $(\omega, \omega,\dots) \in X$ has no countable neighborhood.

spaces/S000174/properties/P000139.md

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+---
+space: S000174
+property: P000139
+value: true
+---
+
+The point $p := (0, 0, \dots) \in X$ is isolated via $\{p\} = 0 ^ \omega \cap \omega_1 ^ \omega$.

spaces/S000174/properties/P000197.md

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+---
+space: S000174
+property: P000197
+value: false
+---
+
+The subspace $\omega_1 \times 0^\omega \subseteq X$ is uncountable and discrete.