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user125821
user125821
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Let $X$ be a completely regular space and let $C_k(X)$ be the space of all continuous functions with the compact-open topology. If $X$ is completely metrizable, is the strong dual of $C(X)^*$ the strong projective limit of the spaces $C(K)$, where $K$ is a compact subset of $K$?

Let $X$ be a completely regular space and let $C_k(X)$ be the space of all continuous functions with the compact-open topology. If $X$ is completely metrizable, is the strong dual of $C(X)^*$ the strong projective limit of the spaces $C(K)$, where $K$ is a compact subset of $K$?

Let $X$ be a completely regular space and let $C_k(X)$ be the space of all continuous functions with the compact-open topology. If $X$ is completely metrizable, is the strong dual $C(X)^*$ the strong projective limit of the spaces $C(K)$, where $K$ is a compact subset of $K$?

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user125821
user125821
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Hereditarily ccc spaces Dual of $C(X)$ with the compact open topology

Suppose thatLet $X$ isbe a completely regular space such that every closed subspaceand let $C_k(X)$ be the space of all continuous functions with the compact-open topology. If $X$ satisfiesis completely metrizable, is the countable chain conditionstrong dual of (ccc). Is$C(X)^*$ the strong projective limit of the spaces $X$ separable$C(K)$, where $K$ is a compact subset of $K$?

Hereditarily ccc spaces

Suppose that $X$ is a completely regular space such that every closed subspace of $X$ satisfies the countable chain condition (ccc). Is $X$ separable?

Dual of $C(X)$ with the compact open topology

Let $X$ be a completely regular space and let $C_k(X)$ be the space of all continuous functions with the compact-open topology. If $X$ is completely metrizable, is the strong dual of $C(X)^*$ the strong projective limit of the spaces $C(K)$, where $K$ is a compact subset of $K$?

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user125821
user125821
  • 19
  • 2

Hereditarily ccc spaces

Suppose that $X$ is a completely regular space such that every closed subspace of $X$ satisfies the countable chain condition (ccc). Is $X$ separable?